WBCS Mains 2019 Official Paper-VI

The ratio of bus and train fares from Burdwan to a certain place is $3:4$. If the train fare increases by $20\%$ and bus fare by $10\%$, then what will be the new ratio of bus and train fares?

When the price of rice increases by $12\frac{1}{2}\%$, a man can get $250\text{gm}$ less rice for $\text{Rs. }18$. Find the present cost of rice per kg.

Of four numbers, the second number is $20\%$ more than the first, the third is $10\%$ less than the second and the fourth number is $50\%$ more than the third. If the fourth number is $405$, find all the numbers.

The expenses for rice, fish and oil of a family are in the ratio $12:17:3$. The prices of these articles are increased by $20\%$, $30\%$ and $50\%$ respectively. By what percent will the total expenses for these articles of the family be increased?

In a certain examination, a candidate answered $25$ questions and two-fifth of the rest of the total number of questions, and he found that he has answered only $60\%$ of the total number of questions. How many questions did he answer?

A man saves $20\%$ of his income. If his expenses are increased by $35\%$, by what percent must his income be raised so that he can save $10\%$ of his new income?

A mixture of milk and water contains $12\frac{1}{2}$ of water. How much water should be added to $200\text{gallons}$ of such a mixture so that the new mixture may contain $37\frac{1}{2}$ of water?

One litre of spirit which contains $10\%$ of water is added to $3\text{litres}$ of spirit containing $7\%$ of water, and to this mixture half a litre of water is added. Find the percentage of water in the final mixture.

A certain kind of brass is composed of copper, zinc, lead and tin. The ratio of copper to zinc is $1:2$, of zinc to lead is $3:5$ and of lead to tin is $7:8$. Find the quantity of each metal in $213\text{gm}$ of brass.

If $25$ men can weave $120\text{metres}$ of cloth in a day, how many metres of cloth will be woven by $35$ men in a day?

$12$ men can do a piece of work in $30$ days. How many extra men should be engaged to do the work in $20$ days?

A man and a boy can do a piece of work in $36$ days. If the man works alone for the last $10$ days, the work is completed in $40$ days. How long would the boy take to do it alone?

$A$ and $B$ together can do a piece of work in $25$ days. If $B$ works alone for the last $10$ days, it is completed in $30$ days. In how many days can $A$ alone do it?

$1200$ boys and $600$ girls are examined in a test. $42\%$ of the boys and $30\%$ of the girls passed. Find the percentage of those who failed.

If $50$ men do a piece of work in $12$ days working $8\text{hours}$ a day, how many hours a day would $60$ men have to work in order to do another piece of work twice as great in $16$ days?

A contractor undertook to finish a road $12\text{km}$ long in $350$ days. But after employing $45$ men for $200$ days, he found that only $4\text{km}$ of the road had been built. How many additional men must be engaged to finish the work in the given time?

A laboratory has to pay $\text{Rs. }67.50$ for $30$ days as a gas bill if it uses $35$ gas burners for $6\text{hours}$ a day. Find the amount to be paid if it uses $30$ gas burners for $18$ days working $7\text{hours}$ a day.

The cost of printing a magazine of $540$ pages with $30$ lines on each page and $15$ words in each line is $\text{Rs. }7200$. Find the cost of printing a magazine of $450$ pages with $35$ lines on each page and $18$ words in each line.

If $a$, $b$, $c$ and $x$ are the 1st, 2nd, 3rd and the 4th proportions respectively, then the value of $x$ will be:

The number $\sqrt{7}$:

Simplify the following expression:

If the ratio of cost price and selling price is $25:26$, then what is the percentage of profit?

There is some loss if an article is sold at $\text{Rs. }120$. There is same amount of profit if the article is sold for $\text{Rs. }140$. What is the cost price of the article?

A man sold a stove for $\text{Rs. }423$ and incurred a loss of $6\%$. At what price should it be sold so as to earn a profit of $8\%$?

A man sold an article at a gain of $5\%$. Had he sold it for $\text{Rs. }240$ more, he would have gained $8\%$ . Find the cost price of the article.

The ratio of manufacturing cost of two saris is $2:5$. If the first sari is sold at $15\%$ profit and the second sari is sold at $18\%$ profit, then the manufacturer makes a total profit of $\text{Rs. }396$. Find the cost of manufacture of the first sari.

A book seller allowing a $12\%$ discount on the marked price of a book made a profit of $10\%$. What will be his percentage of profit if he sells the book at the marked price?

A trader sold a bicycle at a profit of $10\%$. Had he bought the bicycle at $10\%$ less price and sold it at a price $\text{Rs. }12$ more, he would have gained $25\%$. What is the cost price of the bicycle?

A businessman blends Assam tea costing $\text{Rs. }70$ per kg with Darjeeling tea costing $\text{Rs. }110$ per kg in the ratio $3:1$. What should be the selling price per kg of the new mixture to have a profit of $12\frac{1}{2}\%$ for him?

There is a loss of $11\%$ if an article is sold at $\text{Rs. }178$. At what price should it be sold to make a profit of $11\%$?

A retailer getting a discount of $20\%$ on the marked price sells an article at the marked price. The percentage of profit of the retailer is:

A fruit seller purchased bananas at $\text{Rs. }30$ per dozen and sold each pair at $\text{Rs. }7$. What is the percentage profit or loss at this?

Selling a radio at $\text{Rs. }363.75$, there was a loss of $3\%$ to a radio seller. At what price should he sell the radio to make a profit of $10\%$?

A businessman purchased $35\text{kg}$ of pulse at $\text{Rs. }525$ and sold each kg at the rate of $\text{Rs. }18$. What is his percentage of profit or loss at this?

A hawker purchases some mangoes at the rate of $9$ mangoes for $\text{Rs. }5$ and sells them at $\text{Rs. }8$ per dozen. What will be his profit or loss percentage?

A businessman sold an article at a loss of $15\%$. Had he sold the article at $\text{Rs. }100$ more, he would have gained $10\%$. At what price did he sell the article?

In what ratio should Assam tea at $\text{Rs. }40$ per kg and Darjeeling tea at $\text{Rs. }65$ per kg be mixed and sold at $\text{Rs. }60$ per kg to make an overall profit of $25\%$?

A milkman mixed water with $60\text{litres}$ of pure milk and sold the mixture at the cost price, thereby making a profit of $25\%$. Find the quantity of water in the mixture.

A shoemaker sold two pairs of shoes at the same price. On the first pair he makes a profit of $20\%$ and on the other pair he makes a loss of $20\%$. What is his percentage of profit or loss in the whole business?

Paban incurred a $10\%$ loss by selling lemons at $\text{Rs. }18$ per dozen. At what price should he sell each dozen of lemons to make a profit of $10\%$?

There is $25\%$ profit if an article is sold at Rs. $150$. At what per cent should the selling price be increased so that there will be $30\%$ profit?

A sum of money doubles itself in $8$ years at some rate of simple interest. In how many years would it triple itself?

A sum of amounts will be doubled in $7\frac{1}{2}$ years. What is the rate per cent?

A sum amounts to Rs. $1180$ in $3$ years and to Rs. $1300$ in $5$ years. Find the rate of interest.

A certain sum amounts to Rs. $17,200$ at $12\%$ simple interest per annum in a period in which Rs. $22,080$ amounts to Rs. $37,536$ at $14\%$ simple interest per annum. Find the sum.

Ten copies of the book can be bought for a certain sum of money payable at the end of $2$ years. $12$ copies of the same book can be bought for the same sum in ready cash. What is the rate of interest per annum?

Sita deposited some money in a bank at the rate of simple interest of $5.25\%$ per annum. After $2$ years, she has got Rs. $840$ as interest. Calculate the money she has deposited into the bank.

Calculate the number of years for which the interest of Rs. $600$ at the rate of simple interest of $8\%$ per annum will be Rs. $168$.

At the same rate of simple interest per annum, if a principal becomes the amount of Rs. $7100$ in $7$ years and of Rs. $6200$ in $4$ years, determine the principal amount.

A weaver cooperative society takes a loan of Rs. $15,000$ for buying a power loom. After $5$ years, the society has to repay Rs. $22,125$ for recovering the loan. Find the rate of simple interest per annum.

If the total interest becomes Rs. $x$ for a principal having the rate of simple interest of $x\%$ per annum for $x$ years then, the principal will be:

If a principal becomes twice of its amount in $10$ years, the rate of simple interest per annum is:

Calculate the principal whose monthly interest is Rs. $1$ having the rate of simple interest of $5\%$ per annum.

Write the number of years in which the amount becomes twice of the principal having the rate of simple interest $6\frac{1}{4}\%$ per annum.

The ratio of the principal and the amount (principal along with interest) in $1$ year is $8:9$, the rate of simple interest per annum is:

If $10$ men can do a piece of work in $18$ days, in how many days can $12$ men do it?

Present price of a machine is Rs. $2p$ and if the price of the machine decreases by $2r\%$ in each year, the price of the machine after $2n$ years will be:

A person deposited Rs. $100$ in a bank and got the amount Rs. $121$ for two years, the rate of compound interest per annum is:

Find the rate of compound interest per annum, so that the amount on Rs. $400$ for $2$ years becomes Rs. $441$.

If a sum of money doubles itself at a fixed rate of compound interest per annum in $n$ years, find in how many years it will become four times.

Determine the principal amount that at the rate of $5\%$ compound interest per annum earns a compound interest of $\text{Rs. }615$ after two years.

If the rate of increase in population is $r\%$ per year and the population after $n$ years is $p$, then the population $n$ years before was:

A invested $\text{Rs. }6000$ for $5\text{ months}$ and B invested $\text{Rs. }5000$ for $x\text{ months}$ in a business. If the profits of A and B are equal, find the value of $x$.

Two friends start a business with capitals of $\text{Rs. }16,000$ and $\text{Rs. }24,000$. They earn a total profit of $\text{Rs. }3375$ in a year. How much will each friend get as their share of the profit?

Three friends P, Q and R started a business with capitals of $\text{Rs. }15,000$, $\text{Rs. }10,000$ and $\text{Rs. }25,000$ respectively. At the end of the year, they incur a loss of $\text{Rs. }2,500$. How much will each have to pay to cover the loss?

At the beginning of a year, X and Y jointly start a business with $\text{Rs. }24,000$ and $\text{Rs. }30,000$ respectively. After $5\text{ months}$, X invests an additional $\text{Rs. }12,000$ into the business. If the total profit at the end of the year is $\text{Rs. }14,030$, determine each partner's share of the profit.

X and Y jointly start a business with investments of $\text{Rs. }1200$ and $\text{Rs. }800$ respectively. At the end of the year, Y receives $\text{Rs. }120$ as profit. Find the profit share that X will receive.

X, Y and Z start a business together with a combined investment of $\text{Rs. }7200$. After $1\text{ year}$, X, Y and Z get $\text{Rs. }60$, $\text{Rs. }90$ and $\text{Rs. }120$ respectively as profit. Find the amount invested by Z.

Mr. X invests $\text{Rs. }600$ for $5\text{ months}$ and Y invests $\text{Rs. }500$ for $9\text{ months}$ in a business. In what ratio will the profit be distributed between them?

In a partnership business, the total profit of A and B is $\text{Rs. }2000$. If the capital of A is $\text{Rs. }6000$ and his profit share is $\text{Rs. }1200$, find the capital invested by B.

In a joint business, X invests $\text{Rs. }6000$ for $9\text{ months}$ and Y invests $\text{Rs. }8000$ for a certain number of months. If they receive $\text{Rs. }1800$ and $\text{Rs. }1600$ respectively as profit, find the duration for which Y's capital was invested.

In a joint business, the capitals of A and B are in the ratio $3:4$ and the capitals of B and C are in the ratio $6:5$. If A receives a profit share of $\text{Rs. }450$, find the profit share of C.

In a joint business, the capitals of P, Q and R are in the fractional ratio $\frac{1}{4}:\frac{1}{3}:\frac{1}{2}$. At the end of the year, they make a total profit of $\text{Rs. }3900$. Find the profit share received by R.

M and N can finish a piece of work in $15$ and $20\text{ days}$ respectively. If they complete the entire work working together, find the ratio of their income shares.

If $36\text{ bighas}$ of land can be irrigated in $16\text{ days}$ by a well-pump working $15\text{ hours}$ a day, how many days will it take to irrigate $42\text{ bighas}$ of land using the same pump if it works $10\text{ hours}$ a day?

In a business, P invests $\text{Rs. }12,000$. After some days, Q joins the business with an investment of $\text{Rs. }16,000$. If P and Q receive an equal share of the profit $9\text{ months}$ after Q joined, find the total duration for which P's capital remained invested.

P starts a business with a capital of $\text{Rs. }5000$. After $3\text{ months}$, Q joins with a capital of $\text{Rs. }6000$ and $5\text{ months}$ from the start, R invests $\text{Rs. }8000$. If the total profit at the end of the year is $\text{Rs. }3400$, calculate the amount that each will receive.

S and T start a business with investments of $\text{Rs. }2400$ and $\text{Rs. }1600$ respectively. After one year, if S suffers a financial loss of $\text{Rs. }45$, find the loss incurred by T.

P and Q start a joint business. P invests $\text{Rs. }500$ for $9\text{ months}$ and Q invests a certain sum for $6\text{ months}$. If the total profit made is $\text{Rs. }69$ and Q's share of the profit is $\text{Rs. }46$, find the capital amount invested by Q.

In a joint business, the ratio of the capitals of three partners is $5:7:9$. If the total profit earned in the business is $\text{Rs. }420$, find the share of the third partner.

$A$ and $B$ are equal partners. They admit $C$ and $D$ as partners with $\frac{1}{5}\text{th}$ and $\frac{1}{6}\text{th}$ share respectively. What is the profit sharing ratio of all the partners?

$A$ and $B$ are partners sharing profits in the ratio of $7:3$. They admit $C$ for $\frac{1}{5}\text{th}$ share, which he acquires in equal proportions from both. Find the new profit sharing ratio.

$A$ and $B$ are partners sharing profits in the ratio of $5:4$. They admit $C$ for $\frac{1}{9}\text{th}$ share, which he acquires entirely from $A$. Find out the new profit sharing ratio.

$X$ and $Y$ are partners in a firm sharing profits in the ratio of $3:2$. They admit $R$ as a new partner. $X$ gives $\frac{1}{3}\text{rd}$ of his share while $Y$ gives $\frac{1}{10}\text{th}$ from his share. Calculate the sacrificing ratio.

$P$ and $Q$ are partners sharing profits in the ratio of $3:2$. $P$ surrenders $\frac{1}{6}\text{th}$ of his share and $Q$ surrenders $\frac{1}{4}\text{th}$ of his share in favour of $R$, a new partner. What is the sacrificing ratio?

$S$ and $T$ are partners sharing profits in the ratio of $3:2$. $W$ is admitted as a partner. The new profit sharing ratio of $S$, $T$ and $W$ is $4:3:2$. Find out the sacrificing ratio.

$P$ and $Q$ were partners sharing profits in the ratio of $3:2$. They admit $R$ and $S$ as new partners. $P$ surrenders $\frac{1}{3}\text{rd}$ of his share in favour of $R$ and $Q$ surrenders $\frac{1}{4}\text{th}$ of his share in favour of $S$. Calculate the new profit sharing ratio of $P$, $Q$, $R$ and $S$.

$A$ and $B$ are partners sharing profits in the ratio of $7:5$. They agree to admit $C$, their manager, into partnership, who is to get $\frac{1}{6}\text{th}$ share in profits. He acquires his share as $\frac{1}{24}\text{th}$ from $A$ and $\frac{1}{8}\text{th}$ from $B$. Calculate the new profit sharing ratio.

$A$, $B$ and $C$ are partners in a firm sharing profits in the ratio of $4:3:2$. They admit $D$ as a new partner. $A$, $B$ and $C$ each surrendered $\frac{1}{3}\text{rd}$ of their shares in favour of $D$. Calculate the new profit sharing ratio of $A$, $B$, $C$ and $D$.

$A$ and $B$ are in partnership sharing profits and losses in the ratio of $3:2$. They admit $C$ as a new partner. Calculate the new profit sharing ratio if $C$ purchases $\frac{1}{10}\text{th}$ share from $A$.

$A$ and $B$ are partners in a firm sharing profits and losses in the ratio of $5:3$. They admit $C$ as a partner for $\frac{1}{4}\text{th}$ share in the profits of the firm. Calculate the new profit sharing ratio of $A$, $B$ and $C$ if $C$ acquires his share as $\frac{1}{5}\text{th}$ from $A$ and $\frac{1}{20}\text{th}$ from $B$.

Evaluate the following expression:
$$\frac{3}{\sqrt{3}}-\frac{4}{\sqrt{7}+\sqrt{3}}+\frac{1}{\sqrt{12}+3}$$

What least number must be added to $8275$ to make the sum a perfect square?

What least number must be subtracted from $732$ to make the remainder a perfect square?

By what number must $192$ be multiplied, so that the product may be a perfect square?

By what least number must $1260$ be divided to make the quotient a perfect square?

The boys of a school can be arranged in $15$, $18$ or $24$ equal rows and also into a solid square. Find the least number of boys in the school.

$P$ 's age is $\frac{3}{4}\text{th}$ of $Q$ 's age and $R$ 's age is $\frac{1}{12}\text{th}$ of $Q$ 's age. If the age of $R$ is $30$ years, find the age of $P$.

The ratio of two numbers is $3:4$ and their L.C.M. is $180$. Find the numbers.

The ratio of two numbers is $5:8$ and their difference is $69$. Find the numbers.

Find the missing term in the following series:
$$1,6,15,?,45,66,91$$

Find the missing term in the following series:
$$11\frac{1}{9},12\frac{1}{2},14\frac{2}{7},16\frac{2}{3},\dots$$

In the series $2,6,18,54,\dots$, what will be the $8^{\text{th}}$ term?

Find the incorrect term in the following series:
$$380,188,92,48,20,8,2$$

Find the next term in the series: $\text{BMO, EOQ, HQS, ?}$

Infrared is to Heat as Ultraviolet is to ______

Select the lettered pair that has the same relationship as the original pair of words:
$$\text{Sip : Gulp}$$

Select the lettered pair that has the same relationship as the original pair of words:
$$\text{Deplete : Enervate}$$

Select the lettered pair that has the same relationship as the original pair of words:
$$\text{Lugubrious : Sorrowful}$$

Select the lettered pair that has the same relationship as the original pair of words:
$$\text{Incandescent : Glowing}$$

Select the lettered pair that has the same relationship as the original pair of words:
$$\text{Annihilation : Fire : : Cataclysm : ?}$$

Select the lettered pair that has the same relationship as the original pair of words:
$$\text{Paw : Cat : : Hoof : ?}$$

Select the lettered pair that has the same relationship as the original pair of letters:
$$\text{MAN : PDQ : : WAN : ?}$$

Choose the word which is the least like the other words in the group:

Choose the odd one out from the options given below:

Choose the odd one out from the options given below:

Find the odd one out from the options given below:

Choose the word that is structurally or contextually different from the rest:

If GOLD is coded as HOME, COME is coded as DONE and CORD is coded as DOSE, how would you code SONS?

If in a certain language, $\text{CHARCOAL}$ is coded as $45164913$ and $\text{MORALE}$ is coded as $296137$, how is the word $\text{ALLOCHRE}$ coded in that language?

If 'air' is called 'green', 'green' is called 'blue', 'blue' is called 'sky', 'sky' is called 'yellow', 'yellow' is called 'water' and 'water' is called 'pink', then what is the colour of clear sky?

In a certain code language, 'si po re' means 'book is thick', 'ti na re' means 'bag is heavy', 'ka si' means 'interesting book' and 'de ti' means 'that bag'. What should stand for 'that is interesting' in that code language?

Consider the following statements:
(i) 'kemp lamp tems' means 'speak the truth';
(ii) 'bis tim nak' means 'always seek knowledge';
(iii) 'tim tems sik' means 'knowledge is truth';
(iv) 'lik bis zap' means 'never seek violence'.

Which letter code stands for 'always'?

Introducing Reena, Monika said, "She is the only daughter of my father's only daughter". How is Monika related to Reena?

Given that:
(i) A is the mother of B
(ii) C is the son of A
(iii) D is the brother of E
(iv) E is the daughter of B

The grandmother of D is:

A is the brother of B, B is the daughter of C and D is the father of A, then how is C related to D?

Ravi and Kunal are good in Hockey and Volleyball. Sachin and Ravi are good in Hockey and Baseball. Gaurav and Kunal are good in Cricket and Volleyball. Sachin, Gaurav and Michael are good in Football and Baseball. Who is good in Hockey, Cricket and Volleyball?

Six students A, B, C, D, E and F are sitting in the field. A and B are from Delhi while the rest are from Bangalore. D and F are tall while others are short. A, C and D are girls while others are boys. Who is the tall girl from Bangalore?

A, P, R, X, S and Z are sitting in a row. S and Z are in the centre and A and P are in the ends. R is sitting on the left of A. Then who is sitting on the right of P?

Alka is older than Mala, Gopal is older than Mala but younger than Alka. Kapil is younger than Ram and Mala. Mala is older than Ram. Whose age is between Gopal and Ram?

I am facing south. I turn right and walk $20\text{m}$. Then I turn right again and walk $10\text{m}$. Then I turn left and walk $10\text{m}$ and then turning right walk $20\text{m}$. Then I turn right again and walk $60\text{m}$. In which direction am I from the starting point?

Kailash walks $3\text{km}$ to East and turns South and walks $4\text{km}$. Again turns West and walks $6\text{km}$. How far is he from the starting point?

Based on a standard Venn diagram set where three intersecting circles represent "Chinese", "Painters", and


Choose the letter of the region which correctly represents the statement:
Chinese who are painters but not Musicians

Based on a standard Venn diagram set where three intersecting circles represent "Chinese", "Painters", and


Choose the letter of the region which correctly represents the statement:
Painters who are neither Chinese nor Musicians

Based on a standard Venn diagram set where three intersecting circles represent "Chinese", "Painters", and


Choose the letter of the region which correctly represents the statement:
Chinese who are Musicians but not Painters

Based on a standard Venn diagram set where three intersecting circles represent "Chinese", "Painters", and


Choose the letter of the region which correctly represents the statement:
Chinese who are Painters as well as Musicians

Which of the following words will come second in the English dictionary?

The jumbled letters of a meaningful English word are given as YPCUIAT. Rearrange these letters to form a meaningful word and select the alternative that is almost opposite in meaning (antonym) to it.

Rearrange the jumbled letters to form a meaningful word and select the option that is almost opposite in meaning to the rearranged word:
$$\text{SAYMTNE}$$

Rearrange the jumbled letters to form a meaningful word and select the option that is almost opposite in meaning to the rearranged word:
$$\text{MRPBLOE}$$

Nitin ranks eighteenth from the top in a class of $49$ students. What is his rank from the last?

If $\text{P}$ denotes $+$, $\text{Q}$ denotes $-$, $\text{R}$ denotes $\times$, and $\text{S}$ denotes $÷$, which of the following statements is mathematically correct?

Arrange the following human body components in a logical order from bottom to top (distal to proximal):
1. Shoulder
2. Wrist
3. Elbow
4. Palm
5. Finger

A waiter's total income consists of his base salary and tips. During a specific week, his tips amounted to $\frac{5}{4}$ of his base salary. What fraction of his total weekly income came from his tips?

Find the missing term that completes the pattern established in the following number grid:

If on a highly demanding day you are the only employee available at the workplace to handle the entire rush of customers, you should:

Statements:
1. All men are married.
2. Some men are educated.

Conclusions:
I. Some married are educated.
II. Some educated are married.

Statements:
1. Some papers are pens.
2. Angle is a paper.

Conclusions:
I. Angle is not a pen.
II. Angle is a pen.

Statement: 'Smoking is injurious to health' - A mandatory warning printed on cigarette packets.
Assumptions:
I. People read printed matter on a cigarette packet.
II. People take careful note of a warning.
III. Non-smoking promotes health.

Statement: The Reserve Bank of India has directed banks to refuse fresh loans to major intentional defaulters.
Assumptions:
I. The banks may still give loans to the defaulters.
II. The defaulters may repay the earlier loans to get fresh loans.
III. The banks may recover the bad loans through such harsh measures.

Consider a standard geometric square with both of its internal major diagonals drawn completely from corner to corner. Count the total number of independent triangles formed inside this configuration.

Which of the following letter combinations will appear completely identical and unchanged when viewed in a plane mirror?

On a standard six-faced dice, the letters $a,b,c$ and $d$ are written on the four adjacent side faces in a consecutive clockwise direction, while the letters $e$ and $f$ are positioned on the top and bottom faces respectively. If face $c$ is turned to become the top face, which letter will appear on the bottom face?

Study the following layout information:
* Tree $\text{E}$ is located to the North-East of tree $\text{B}$.
* Tree $\text{A}$ is situated $15\text{ m}$ exactly to the East of tree $\text{B}$.
* Tree $\text{B}$ is situated $40\text{ m}$ exactly to the West of tree $\text{D}$.
* Tree $\text{C}$ is to the North-West of tree $\text{A}$ and lies directly on the straight line connecting $\text{B}$ and $\text{E}$.
* Tree $\text{A}$ is located $30\text{ m}$ directly to the South of tree $\text{E}$.

What is the linear straight-line distance between tree $\text{A}$ and tree $\text{D}$?

Study the following layout information:
* Tree $\text{E}$ is located to the North-East of tree $\text{B}$.
* Tree $\text{A}$ is situated $15\text{ m}$ exactly to the East of tree $\text{B}$.
* Tree $\text{B}$ is situated $40\text{ m}$ exactly to the West of tree $\text{D}$.
* Tree $\text{C}$ is to the North-West of tree $\text{A}$ and lies directly on the straight line connecting $\text{B}$ and $\text{E}$.
* Tree $\text{A}$ is located $30\text{ m}$ directly to the South of tree $\text{E}$.

In which direction is tree $\text{E}$ situated with respect to tree $\text{D}$?

The area of a triangle is exactly equal to the area of a square whose side measures $75\text{ meters}$. Find the base length of this triangle if its corresponding altitude is $125\text{ meters}$.

In a certain code language, the word 'BASKET' is written as '5 $ 3 % # 1' and 'TRIED' is written as '1 4 * # 2'. How is the word 'SKIRT' written in that identical code language?

The position of the first and the fifth digits of the number $81943275$ are interchanged. Similarly, the position of the second and the sixth digits are interchanged, and so on until the fourth and the eighth digits are interchanged. Which digit will be the third digit from the right end after this complete rearrangement?