WBCS Mains 2020 Official Paper-VI

$8$ men or $12$ women can do a piece of work in $20$ days. The number of days needed to complete the job, if $10$ men and $15$ women are employed to do the same piece of work is:

Raju invested $\text{Rs. }15,000$ in two parts. One part at $8\%$ and the other at $12\%$ per annum. His total annual income from interest is $\text{Rs. }1640$. The ratio of the two parts respectively is:

If a sum of money doubles itself at compound interest in $12$ years, in how many years will it become four times?

Successive discounts of $x\%$ and $y\%$ are equivalent to a single discount of:

Gold and Copper are heavier than water by $19$ and $9$ times respectively. In what proportion should they be mixed to form an alloy so that it will be heavier than water by $15$ times?

The compound interest on $\text{Rs. }10,000$ in $2\frac{1}{2}$ years at $10\%$ per annum is:

If $a=2021$, $b=2022$, and $c=2023$, then the value of $a^3+b^3+c^3-3abc$ is:

The marked price of a pen is $\text{Rs. }200$ and a customer buys it for $\text{Rs. }153$ after two successive discounts. If the first discount is $10\%$, then the second discount is:

If $\alpha$ and $\beta$ are the roots of the quadratic equation $a{x}^2+2bx+c=0$ and $\alpha +\gamma$, $\beta +\gamma$ are the roots of $A{x}^2+2Bx+C=0$, then which one of the following is correct?

A bus travels from Kolkata to Digha at the rate of $55\text{km/hour}$ and returns at the rate of $66\text{km/hour}$. Then the average rate of the whole journey is:

Rahul's salary is first increased by $10\%$ and then again by $20\%$. But due to COVID-19, the salary is decreased by $25\%$. By what percent does the initial salary change?

A man buys two types of oranges equal in number, one at $5$ for a rupee and the other at $3$ for a rupee, and sells the entire lot at $6$ for $\text{Rs. }2$. His gain or loss percent is:

A train travels at a speed of $30\text{km/hour}$ for $12$ minutes and then for the next $8$ minutes at a speed of $45\text{km/hour}$. The average speed for the entire journey is:

If $\tan 2\theta \tan \theta =1$, then the value of $\tan 2\theta$ is:

$\Delta ABC$ is a triangle where $\angle C=90^{\circ }$. If $p$ is the length of the perpendicular from $C$ to $AB$, then $\frac{1}{B{C}^2}+\frac{1}{A{C}^2}=$

Sneha wants to buy a piece of furniture worth $\text{Rs. }12,500$. She gets a discount of $10\%$ on it. After getting the discount, she pays $18\%$ GST. Find the total amount she will have to pay for the furniture.

If $2x^2+5y^2+2z^2-2xy-6yz=0$, then $x:y:z$ is:

A pipe can fill a tank in $16$ hours. Due to a leak in the bottom, it is instead filled in $24$ hours. If the tank is completely full, how much time will the leak take to empty it?

A man travels three-fifth of a distance $AB$ at a speed of $3x$ and the remaining distance at a speed of $2y$. If he goes from $B$ to $A$ and returns at a uniform speed of $5z$ in exactly the same total time, then which one of the following relations is correct?

A man buys milk at $\text{Rs. }60$ per litre, adds water to it, and then sells the mixture at $\text{Rs. }50$ per litre. What is the ratio of milk and water if his profit in the deal is $20\%$?

Avishek sells a book at a profit of $20\%$. If he had bought it at $20\%$ less and sold it for $\text{Rs. }18$ less, he would have gained $25\%$. The cost price of the book is:

If $a^2+b^2+c^2=ab+bc+ca$, then which one is correct?

Ram and Shyam solve a quadratic equation. Ram makes a mistake in the constant term and finds the roots as $5,-3$. Shyam makes a mistake in the co-efficient of $x$ and gets the roots as $1,-3$. The correct roots are:

$\text{Rs. }6000$ is divided among $40$ boys and some girls so that each boy gets $\text{Rs. }100$ and each girl gets $\text{Rs. }250$, then the number of girls is:

A man gets a simple interest of $\text{Rs. }3500$ on a certain principal at the rate of $10\%$ per annum in $5$ years. What compound interest will the man get on twice the principal in two years at the same rate?

If the first and second of the five numbers in continued proportion are $2$ and $8$ respectively, then the fifth number is:

The simple interest and compound interest of a certain sum of money for two years are $\text{Rs. }400$ and $\text{Rs. }410$ respectively. Then the rate of interest per annum is:

Average age of $8$ sons of a family is $12$ years. Average age of the sons together with their parents is $21$ years. If the father is older than the mother by $8$ years, then the age of the mother is:

Rohit sold two books at $\text{Rs. }60$ each. On one he gains $20\%$ and on the other loses $20\%$. Then he made:

Barun invests $\text{Rs. }5000$ for a year and Tarun joins him with $\text{Rs. }8000$ after six months. After the year they receive a return of $\text{Rs. }4500$, then Tarun's share is:

In a circle touching the side $BC$ of $\Delta ABC$ at $P$ and sides $AB$ and $AC$ produced at $Q$ and $R$ respectively. If $AQ=10\text{cm}$, then the perimeter of $\Delta ABC$ is:

If the semi perimeter of a right-angled triangle be $s\text{cm}$ and hypotenuse be $c\text{cm}$, then the area of the triangle is:

The income of Priya is $40\%$ higher than that of Liza and the income of Disha is $20\%$ less than that of Liza. Income of Priya is higher than income of Disha by:

Three solid spheres of gold whose radii are $1\text{cm}$, $6\text{cm}$ and $8\text{cm}$ respectively are melted into a single solid sphere. Then the radius of the sphere is:

Present ages of Ram and Laxman are in the ratio of $5:4$ respectively. Three years hence, the ratio of their ages will become $11:9$ respectively. What is Laxman's present age?

If $a+b+c=0$, then $\frac{1}{x^b+x^{-c}+1}+\frac{1}{x^c+x^{-a}+1}+\frac{1}{x^a+x^{-b}+1}$ is equal to:

In an examination, $34\%$ of the candidates fail in Bengali and $42\%$ in English. If $20\%$ fail in Bengali and English, the percentage of those passing in both subjects is:

Mohit went to a shop to buy $50\text{kg}$ of rice. He buys two varieties of rice which cost him $\text{Rs. }4.50$ per kg and $\text{Rs. }5$ per kg. He spends a total of $\text{Rs. }240$. What was the quantity of less expensive rice bought by him?

The ratio of syrup and water in $30$ litre of a mixture is $1:5$, then the amount of water required to mix to make the ratio $1:6$ is:

In an examination $75\%$ passed in Maths, $80\%$ passed in Bengali, $65\%$ in both and $45$ students failed in both subjects. Then the number of students appeared are:

A conical container of base diameter $2R$ and height $H$ is full of water which is poured into a cylindrical container of diameter $2pR$. Then it will occupy a height equal to:

If the time taken to go from one station to another is required to be decreased by $20\%$, then by what percent must the speed of the train be increased?

Satyajit is younger than Diganta by $8$ years. If their ages are in the ratio of $5:7$, then how old is Satyajit?

The mean of five observations $x$, $x+2$, $x+6$, $x+4$, $x+8$ is $11$. The mean of the last three observations is:

In a right-angled triangle $\Delta ABC$, $\angle B=90^{\circ }$, $AB=6\text{cm}$, and $BC=8\text{cm}$. The radius $r$ of the inscribed circle is:

A right circular cone, a right circular cylinder and a hemisphere all have the same radius, and the heights of the cone and cylinder equal their diameters. Then their volumes are proportional respectively to:

A merchant purchases $11$ toys for Rs. $10$ and sells $10$ toys for Rs. $11$. His profit percentage is:

A sum of money lent at simple interest becomes double of itself in $8$ years. Then the sum will triple itself in:

An article is sold at Rs. $972$, yielding a profit of $8\%$. If it is sold at Rs. $872$, then there is a loss of:

If $\tan \theta +\sin \theta =m$ and $\tan \theta -\sin \theta =n$, then which one of the following relations is correct?

The simplified value of $\frac{1+984762\times 984764}{984763\times 984763}$ is:

The income from a bus in every trip is Rs. $100$. If the bus fare increases by $50\%$ and the number of passengers decreases by $20\%$, then the income in every trip becomes:

The price of sugarcane rises by $20\%$. By how much percent must a housewife reduce her consumption so that her expenditure remains the same?

The cost price of article A is Rs. $200$ and the selling price of another article B is Rs. $308$. If the selling price of A is equal to the cost price of B, then the profit after selling A is $10\%$. What is the profit percentage on B?

In an election, $15\%$ of voters did not cast their votes. Ratanbabu got $62.5\%$ of the votes cast and was declared elected by a majority of $3400$ votes. Find the total number of voters.

The radius of a solid sphere is $R\text{cm}$. If it is bisected into two identical hemispheres, then the total surface area of the two pieces obtained is:

In a triangle $\Delta PQR$, points $A$, $B$, and $C$ are the midpoints of the sides $PQ$, $QR$, and $RP$ respectively. If the area of the triangle $\Delta ABC$ is $16\text{sq.units}$, then the area of the triangle $\Delta PQR$ is:

The speed of a boat in still water is $8\text{km/h}$. If it can travel $20\text{km}$ downstream and $12\text{km}$ upstream in the same amount of time, the speed of the stream is:

If

is equal to:

The lengths of two parallel chords of a circle are $6\text{cm}$ and $8\text{cm}$. If the smaller chord is at a distance of $4\text{cm}$ from the centre, then the distance of the other chord from the centre is:

If $x=by+cz$, $y=cz+ax$, and $z=ax+by$, then the value of the expression:
$$\frac{a}{1+a}+\frac{b}{1+b}+\frac{c}{1+c}$$

is equal to:

The age of a father today is thrice as that of his son. After $15$ years, the age of the father will be twice that of his son. The age of the son today is:

A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio $8:5$, the ratio of radius to the height is:

$ABCD$ is a cyclic quadrilateral and the sides $DC$ and $AB$ are produced to meet at $P$. If $\angle APD=25^{\circ }$ and $\angle PBC=70^{\circ }$, then $\angle BAD$ is equal to:

The price of coal being increased by $20\%$, a family reduces its consumption of coal by $20\%$. By what percent will the family's expenses for coal increase or decrease?

Ranjan sold his bag to Joydip at a gain of $8\%$ and Joydip sold it to Raju at a gain of $10\%$. If Raju paid $\text{Rs. }297$ for it, the price paid by Ranjan is:

If

then $x$ equals:

While preparing a mixture of tea, $5\%$ of the tea is lost. In what ratio should a trader mix two kinds of tea costing $\text{Rs. }600/\text{kg}$ and $\text{Rs. }450/\text{kg}$ respectively so that he might gain $25\%$ by selling the mixed tea at $\text{Rs. }625/\text{kg}$?

If $u_i=\frac{x_i-25}{10}$, $\sum f_i{u}_i=20$, and $\sum f_i=100$, then find the value of the mean $\bar{x}$.

The lateral surface area of a right circular cone is three times the volume of that cone. If the height and the radius of the cone are $h\text{units}$ and $r\text{units}$ respectively, then $\frac{1}{h^2}+\frac{1}{r^2}$ is equal to:

A hemispherical bowl is made of a steel sheet $0.8\text{cm}$ thick. The inside radius of the bowl is $5\text{cm}$. The volume of steel used in making it is approximately:

If

then which of the following relations is correct?

A person walks from his house at a speed of $4\text{km/h}$ and reaches his school $5$ minutes late. If his speed had been $5\text{km/h}$, he would have reached $10$ minutes earlier. The distance of the school from his house is:

The greatest and the least value of $a+b\sin \theta$ ($0^{\circ }\le \theta \le 90^{\circ }$) are $7$ and $3$ respectively. Find the values of $a$ and $b$.

If $P(1,2)$, $Q(4,6)$, $R(5,7)$, and $S(a,b)$ are the vertices of a parallelogram $PQRS$, then the values of $a$ and $b$ are:

If the radius and height of a cone are each increased by $10\%$, then the volume of the cone is increased by:

If $H$, $S$, and $V$ are the height, curved surface area, and volume of a cone respectively, then find the value of:
$$3\pi V{H}^3+9V^2-S^2{H}^2$$

If the cost price of $12$ articles is equal to the selling price of $10$ articles, then the percentage of profit is:

If $x=\frac{8ab}{a+b}$, then find the value of:
$$\frac{x+4a}{x-4a}+\frac{x+4b}{x-4b}$$

If $\frac{1}{1+x}+\frac{2}{2+y}+\frac{1009}{1009+z}=1$, then the value of $\frac{x}{1+x}+\frac{y}{2+y}+\frac{z}{1009+z}$ is equal to:

A number is increased by $10\%$ and then decreased by $10\%$, then the number

A man invests $\text{Rs. }5000$ at a rate of $6\%$ per annum. How much more should he invest at a rate of $9\%$, so that he can earn a total of $7\%$ per annum?

A sum of money compounded annually becomes $\text{Rs. }500$ in two years and $\text{Rs. }550$ in three years. The rate of interest per annum is

The areas of two similar triangles are $36\text{sq.cm}$ and $81\text{sq.cm}$ respectively. If the median of the smaller triangle is $12\text{cm}$ then the corresponding median of the larger triangle is

If the rate of compound interest for the first year is $4\%$ and for the second year is $5\%$, then the compound interest on $\text{Rs. }25,000$ for $2$ years is

$A$ and $B$ can do a piece of work in $10$ days, $B$ and $C$ in $12$ days, and $C$ and $A$ in $15$ days. The number of days taken by $A$, $B$, and $C$ working together to finish the work is

Pipe $A$ can fill a tank in $3$ hours and pipe $B$ can fill it in $4$ hours. If they are opened at alternate hours and if pipe $A$ is opened first, in how many hours will the tank be filled?

Six years hence, a man's age will be three times the age of his son and three years ago he was nine times as old as his son. The present age of the man is

$76$ ladies can do a job in $33$ days. Due to some reason, some ladies did not join the work and therefore, it was completed in $44$ days. The number of ladies who did not join the work is

In a joint business, the ratio of the capitals of three friends was $\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$. After $4$ months, the first friend withdrew half of his capital and $8$ months thereafter, $\text{Rs. }2024$ was recorded as their total profit. What was the share of profit of the first friend?

The difference between simple interest and compound interest on a sum for $3$ years at $10\%$ when the interest is compounded annually is $\text{Rs. }155$. Then the principal value is

The current population of a town is $120000$. If the population increases by $10\%$ every year, then the population of the town after three years will be

If ${\left(x+\frac{1}{x}\right)}^2=3$, then the value of $x^{2020}+x^{2021}+x^{2022}+x^{2014}+x^{2015}+x^{2016}+1$ is

If $3\sin \alpha +5\cos \alpha =5$, then the value of $(3\cos \alpha -5\sin \alpha {)}^2$ is equal to

Out of $15$ cows, one worth $\text{Rs. }1800$ was removed and a horse was taken in. If their average price is thereby increased by $\text{Rs. }300$, then the price of the horse is

The production of scooters rose to $48400$ from $40000$. If the rate of growth is $10\%$, then the time required is

Two circles with radii $r_1$ and $r_2$ respectively, touch each other externally. Let $R$ be the radius of a circle that touches these two circles as well as their common tangent line. Which of the following relations is true?

Amal invests $\frac{1}{4}$ of his capital at $8\%$ p.a., $\frac{1}{5}$ at $10\%$ p.a., and the remainder at $7\%$ p.a. If his total annual income from interest is $\text{Rs. }628$, then his total capital is

The mean of a frequency distribution is $8.1$. If $\sum f_i{x}_i=132+5k$ and $\sum f_i=20$, then the value of $k$ is

A manufacturer marked an article at $\text{Rs. }120$ and sold it allowing a $15\%$ discount. If his profit was $20\%$, then the prime cost (cost price) of the article is

A boatman goes $2\text{km}$ against the current of the stream in $1\text{hour}$ and goes $1\text{km}$ along the current in $10\text{minutes}$. How long will it take to go $5\text{km}$ in stationary water?

Direction: Study the following alphabetical sequence and answer the question based on it.
$$\text{GAGHUTAAKHGAOYYDKKVRABICDDCRFFAHAHAIH}$$

If we write the letters of the above series in the reverse order, which letter is the middlemost?

What fraction of $\frac{4}{7}$ must be added to itself to make the sum $\frac{15}{14}$?

A man can row upstream at $8\text{kmph}$ and downstream at $13\text{kmph}$. The speed of the stream is:

Direction: Suppose the following words Man, Men, Machine, Method, Methodical, Make, Mentor, Map are arranged according to the dictionary rule. Which of them will be at the start?

Study the following table and answer the question based on it:
**Number of Candidates Appeared, Qualified and Selected in a Competitive Examination from Five States Delhi,


In the year 1997, which state had the lowest percentage of candidates selected over the candidates appeared?

Jaya and Hima are competing in a $200\text{meter}$ race. Both start the race at the same time, but Jaya starts the race $40\text{meters}$ ahead of the starting point, whereas Hima starts the race at the starting point. Assume that Hima runs at a speed of $10\text{meters per second}$, whereas Jaya runs at a speed of $x\text{meters per second}$. If both reach the finish line at the same time, then what is the value of $x$?

Three cubes of edges $6\text{cm}$, $8\text{cm}$ and $10\text{cm}$ are melted without loss of metal into a single cube. The edge of the new cube will be:

Three times the first of three consecutive odd integers is $3$ more than twice the third. The third integer is:

Direction: Study the following alphabetical sequence and answer the question based on it.
$$\text{GAGHUTAAKHGAOYYDKKVRABICDDCRFFAHAHAIH}$$

The number of vowels that are absent in the above series is:

The $5\text{th}$ term in the following series:
$$a{b}^2+b{c}^2+c{d}^2+\dots \text{ to }25\text{ terms will be:}$$

If all the letters of the word RATIONALISATION are written according to the alphabetical order, which letter will be farthest from the first letter?

A and B are at a distance of $800\text{m}$. They start moving towards each other at $20\text{kmph}$ and $24\text{kmph}$ respectively. As they start, a bird sitting on the cap of A starts flying towards B, touches B and then returns towards A and so on, till they meet. What is the distance traveled by the bird, if its speed is $176\text{kmph}$?

A boat running downstream covers a distance of $16\text{km}$ in $2\text{hours}$ while for covering the same distance upstream, it takes $4\text{hours}$. What is the speed of the boat in still water?

When a number is added to seven-ninth of thirty-five per cent of $900$, the resultant is $325$. What is the number?

If the letters in the word "PSCEXAM" are rearranged according to the English alphabetical order, how many letter(s) will remain in the same position after the rearrangement?

Direction: Monica, Amar, Akbar and Anthony live in four apartments that are arranged side by side. Only one of the above four persons is the landlord whose apartment is at one end. Amar's apartment is neither next to Monica's apartment nor next to Akbar's apartment. Monica's apartment is not at one end. Amar is not the landlord.
Who lives just beside the landlord?

A man rows downstream $32\text{km}$ and $14\text{km}$ upstream. If he takes $6\text{hours}$ to cover each distance, then the velocity (in $\text{kmph}$) of the current is:

If one-third of a tank holds $80\text{litres}$ of water, then the quantity of water that half of the tank holds is:

From a group of $7\text{men}$ and $6\text{women}$, five persons are to be selected to form a committee so that at least $3\text{men}$ are there in the committee. In how many ways can it be done?

A shopkeeper gives two successive discounts of $20\%$ and $10\%$ on surplus stock. Further, he also gives $5\%$ extra discount on cash payment. If a person buys a shirt from the surplus stock and pays in cash, what overall discount percent will he get on the shirt?

If the letters in the word "PSCEXAM" are rearranged according to the reverse English alphabetical order, how many letter(s) will remain in the same position after the rearrangement?

A person travels $3.5\text{km}$ from place A to place B. Out of this distance, he travels $\frac{5}{3}\text{km}$ on bicycle, $\frac{7}{6}\text{km}$ on scooter and the rest on foot. What portion of the whole distance does he cover on foot?

The data indicates the distribution of students across seven different institutes (P, Q, R, S, T, U, V). In a standard evaluation of this problem where the total number of graduate students is $27300$ (with R comprising $18\%$) and post-graduate students is $24700$ (with R comprising $13\%$), what is the total number of graduate and post-graduate level students in institute R?

When a ball bounces, it rises to $\frac{3}{4}$ of the height from which it fell. If the ball is dropped from a height of $32\text{m}$, how high will it rise at the third bounce?

Based on the data provided for Punjab over the years 1997 to 2001, find the year in which the percentage of candidates qualified from Punjab over those appeared from Punjab is the highest.

Monica, Amar, Akbar and Anthony live in four apartments that are arranged side by side. Only one of the four persons is the landlord whose apartment is at one end. Amar's apartment is neither next to Monica's apartment nor next to Akbar's apartment. Monica's apartment is not at one end. Amar is not the landlord.
Amar lives:

Consider the following three statements by Amar, Akbar and Anthony:
* Amar: "Anthony is a good boy."
* Akbar: "Amar is a liar."
* Anthony: "I am not a good boy."
You know that at least two of them are telling the truth. Who is/are telling the truth?

If Pamela ranks seventeenth in a class of thirty-one, what is her rank from the last?

Suppose the day after tomorrow is NOT Saturday. Which of the following days CANNOT be the day before yesterday?

Monica, Amar, Akbar and Anthony live in four apartments that are arranged side by side. Only one of the four persons is the landlord whose apartment is at one end. Amar's apartment is neither next to Monica's apartment nor next to Akbar's apartment. Monica's apartment is not at one end. Amar is not the landlord. Who is the landlord?

If $(a,b)\ast (c,d)=(a+d)-\frac{c}{b}$, then $\left(\frac{5}{6},\frac{2}{7}\right)\ast \left(\frac{3}{7},\frac{2}{3}\right)$ will be:

Simplify the expression: ${\log }_{4}3\cdot {\log }_{243}64$

If the current ratio of the father's age to the son's age is $4:1$ and the product of their ages is $256$, what will be the ratio of their ages after $5$ years?

Monica, Amar, Akbar and Anthony live in four apartments that are arranged side by side. Only one of the four persons is the landlord whose apartment is at one end. Amar's apartment is neither next to Monica's apartment nor next to Akbar's apartment. Monica's apartment is not at one end. Amar is not the landlord. Monica lives:

If ${}^n{P}_r=n(n-1)(n-2)\cdots (n-r+1)$ and ${}^n{P}_3=24$, then the value of $n$ will be:

Study the following alphabetical sequence:
$$\text{G A G H U T A A K H G A O Y Y D K K V R A B I C D D C R F F A H A H A I H}$$

How many vowels are there in the above series which are immediately preceded by a consonant?

In a certain code language, "PREMONITION" is coded as $68530492904$. How will you write "MONITOR" in that same code language?

Arrange the following words according to standard dictionary rules: "Man", "Men", "Machine", "Method", "Methodical", "Make", "Mentor", "Map". Which of them will be at the end?

What is the smallest number which when decreased by $8$ is exactly divisible by $21$, $27$, $33$ and $55$?

Out of the two bar graphs provided, one shows the amount (in Lakh $\text{Rs.}$) invested by a Company in purchasing raw materials over the years and the other shows the values (in Lakh $\text{Rs.}$) of finished goods sold by the Company over the years.



The value of sales of finished goods in 1999 was approximately what percent of the sum of the amount invested in Raw materials in the years 1997, 1998, and 1999?

The following distribution represents the overseas tourist traffic from India:



What percentage of Indian tourists went to either USA or UK?

A box contains $15$ marbles out of which $4$ are white, $5$ are red and $6$ are blue. Three balls are to be drawn at random from the bag. What is the probability that all of them are red?

In a certain code language:
* $123$ means 'sober nice lady'
* $356$ means 'nice sunny day'
* $589$ means 'a rainy day'

Which of the following numeral stands for 'sunny'?

The average weight of $8$ persons increases by $2.5\text{kg}$ when a new person comes in place of one of them weighing $65\text{kg}$. What might be the weight of the new person?

The difference between a two-digit number and the number obtained by interchanging the digits is $36$. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is $1:2$?

Ankit is the son of Zubin. Manju is the daughter of Anil. Sheela is the mother of Manju. Mohan is the brother of Manju. How is Mohan related to Sheela?

A sum of $\text{Rs. }312$ was divided among $100$ boys and girls in such a way that each boy gets $\text{Rs. }3.60$ and each girl $\text{Rs. }2.40$. The number of girls is:

A two-digit number is such that the product of the digits is $8$. When $18$ is added to the number, then the digits are reversed. The number is: