Arithmetic Questions

P and Q can do a piece of work in 36days, Q and R can do it in 60days, and P and R can do it in 45days. When P, Q and R work together, how much work is finished by them in 5days?

A bought an item for ₹1,100 and sold it to B at a loss of 5%. B sold the item to C at a profit of k% for ₹1,254. Find the value of k.

A man can row a boat at 10km/h in still water. If the speed of the stream is 7km/h, what is the time taken to row a distance of 85km down the stream?

A bus covers the first 80km at a speed of 40km/h. It covers the next 100km at a speed of 50km/h. What is its average speed?

C and B can do a work in $18$ days and $24$ days respectively. They worked together for $8$ days and then C left. In how many days did B finish the remaining work?

The population of a village increases by 6.25% every year. If the present population of the village is 4046, then what was its population 2 years ago?

At a college NSS camp, there is food provisions for 320 students for 38days. If 60 more students join the NSS camp on the first day itself, then for how many days will the provisions last?

On selling 2800 school bags, Anita earns a profit equal to the sale price of 420 school bags. What is the gain percentage that Anita earned?
Note: round off to two decimal places

There are six numbers whose average is 120. If the sixth number is one-fourth of the sum of the remaining five numbers, then the sixth number is:

The third proportional to 7
6
1
​
and 11 is:

A person covers a distance of 40km by bus in 70mins. After deboarding the bus, he took a rest for 40mins and covered another 20km by taxi in 40mins. Find his average speed for the whole journey.

If $\text{Rs. }1,500$ is invested at $5\%$ per annum compounded annually, what will be the total amount after $2\text{ years}$?

A teacher records the test scores of five students in two different subjects. The scores are as follows:
* Maths: $78,85,92,88,76$
* Science: $82,79,91,87,84$

Calculate the average score for each subject.

A sum of money becomes three times at $5\%$ per annum simple interest. At what rate $\%$ will it become six times in the same time?

A and B each can do a work in $75$ days. They began the work together but A left after some time and B completed the remaining work in $23$ days. After how many days of the start of the work did A leave?

A can finish one-third of a work in 5 days, and B can finish 50% of the same work in 15 days. If they work together, then in how many days will they finish 50% of the work?

If the selling price of 10 chairs is the same as the cost price of 8 chairs, find the loss percentage.

In a mixture of milk and water, the ratio of milk to water is $5:2$. If the total mixture is $35\text{ litres}$, how many litres of milk does it contain?

At $12\%$ simple interest per annum, Sunitha lent $\text{Rs. }4,000$ to Rohan for $3\text{ years}$ and $\text{Rs. }5,000$ to Priyanka for $2\text{ years}$. Calculate the total interest Sunitha earned from both loans.

Find the simple interest on Rs. 3,500 at 10% p.a. for 7 years.

John invests $\text{Rs. }18,000$ in stocks and Sarah invests $\text{Rs. }1,00,000$ in stocks. What is the ratio of John's investment to Sarah's investment?

A car travels the following distances on four consecutive days:
* Day 1: $120\text{km}$
* Day 2: $95\text{km}$
* Day 3: $145\text{km}$
* Day 4: $140\text{km}$

What is the average distance covered per day?

Two numbers are in the ratio of $3:7$. If $11$ is subtracted from each, the ratio between the numbers becomes $7:20$. Find the smaller number.

Ram buys 13 balls for Rs. 390 and sells them at the rate of Rs. 33 per ball. Find his gain percentage.

The scores of a cricket team in five matches are given as $165,210,185,240,$ and $175$. If the team needs a combined average score of $200\text{ runs}$ across six matches to qualify, how many runs must it score in the sixth match?

Which least number should be subtracted from 5825 to make it a perfect square?

The average of 37 numbers is 80. The average of the first 19 numbers is 75 and the average of the last 19 numbers is 84. If the 19
th
number is excluded, what is the average of the remaining numbers (approximate to one decimal place)?

A number is increased by 20%, then decreased by 27%, and then further increased by 10%. What is the net increase/decrease percentage in the number (correct to the nearest integer)?

A man's pension on retirement from service is equal to half the average salary during the last $3$ years of his service. His salary from 1-1-1983 is $\text{₹}380$ per month, with increment of $\text{₹}40$ due on 1-10-1983, 1-10-1984 and 1-10-1985. If he retires on 1-1-1986, what pension does he draw per month?

$57\%$ of Ranita’s weekly income is equal to $76\%$ of Bhaskar’s weekly income. If Ranita’s weekly income was reduced by $\text{₹}400$, while Bhaskar’s weekly income did not change, the ratio of the weekly incomes of Ranita and Bhaskar, respectively, would have been $6:5$. What is Bhaskar’s weekly income (in $\text{₹}$)?

The bodyweight of eight members of a club is recorded as 69kg, 63kg, 72kg, 76kg, 82kg, 93kg, 59kg, and 55kg. What is the average body weight of all the eight members?

The ratio of the incomes of A and B is 2:3 and the ratio of their expenditures is 5:7. If 7 times the income of A is equal to $6 times the expenditure of B, then what is the ratio of the savings of A and B?

A man buys 120 toys each at the same cost price. He sells 45% of the toys at 40% profit, one-third of the remaining at 20% profit, and the remaining at a loss which is equal to the cost price of 14 toys. His profit per cent in the entire transaction is:

6 men earn as much as 7 women, 2 women earn as much as 3 boys, 4 boys earn as much as 5 girls. If 5 girls earn Rs. 400 a week, how much does a man earn in a week?

A certain sum invested at simple interest amounts to Rs. 10,072 in 3
2
1
​
years and to Rs. 11,552 in 6 years at the same rate per annum. The rate of interest p.a. is:

Paulson usually leaves his home everyday at 8:15 am and travels at a certain speed to reach office on time. One day he travelled at $\frac{3}{5}$ of the usual speed and hence arrived 45 minutes late. How much time does Paulson usually take to reach his office?

In an election between two candidates, one got $60\%$ of the total valid votes. $25\%$ of the votes were invalid. If the total number of votes was $15,000$, then find the number of valid votes that the other candidate got.

A man invested a total of Rs. 16,50,000 in the names of his two daughters aged 15 years and 17 years, respectively, such that they get equal amounts when they are 20 years old. If the rate of interest is 25% per annum, compounded annually, then how much money (in Rs., to the nearest tens) should be deposited in the name of his younger daughter?

The average marks obtained by a group of $25$ students was $24$. One student left the group as a result of which the average of the remaining students rose to $25$. But another student came in as a result of which the average marks of the group dropped a bit and became $24.8$. What was the average marks obtained by the student who left and the one who joined later?

Abhay and Shreya can individually complete a piece of work in $42\text{ mins}$ and $70\text{ mins}$ respectively. Starting with Abhay, they work alternately for a minute each till the work is completed, with only the one working at the end being allowed to work for less than a minute in the final turn. How long will it take the duo to complete the work?

Which of the numbers given below is exactly divisible by 12?

If $70\%$ of a number is $0.35$, then find $120\%$ of that number.

The batting average for $30$ innings of a cricket player is $40$ runs. His highest score exceeds his lowest score by $100$ runs. If these two innings are not included, the average of the remaining $28$ innings is $38$ runs. Then the lowest score of the player is:

A person borrowed $\text{₹}1760$ at $6\%$ per annum and $\text{₹}2240$ at $9\%$ per annum at simple interest for the same period. He had to pay $\text{₹}1536$ in all as interest. Find the time (in years).

Rishika and Akash invested some money each in a partnership. Rishika had invested $\text{₹}1875$ and took home $\text{₹}225$ as her share from the profit made. If Akash took home $\text{₹}288$ as his share of the profit made, then how much had Akash invested?

$78\%$ of $450$ is:

By selling an item for $\text{₹}198$, Souvik made a loss of $12\%$. By how much should he have raised the price to make a profit of $8\%$?

If $x:4::y:5$, then $x:y$ is:

Refer to the data table below and answer the following question.
(Note: Figures given are in lakh rupees)

Company 2011 2012 2013 2014 2015
Company A 2000 2000 5000 2000 1000
Company B 2000 3000 1000 5000 2000
Company C 3000 2000 5000 3000 3000
For which of the following pairs of years are the total exports from the three Companies together equal?

What annual instalment will discharge a debt of ₹ 10,192 due in 3 years at 10% simple interest?

A car covers $20\text{km}$ in the first quarter of an hour, $25\text{km}$ in the second quarter of that hour and $15\text{km}$ in the third quarter. The average speed of the car (in $\text{km/h}$) over the entire journey is:

If a rope $154\text{ m}$ long is divided in the ratio $9:5$, then the length of the shorter piece (in $\text{m}$) is:

Raksha can complete a piece of work in $12\text{ days}$ while Esther takes $20\text{ days}$ to complete the work. They start working together but Raksha leaves $4\text{ days}$ before the work gets over. For how many days does Esther work?

The bus fare between two cities is increased in the ratio 1:2. Find the increase in the fare, if the original fare is Rs. 175.

Anju sold an article to her friend Rakesh at 14% loss. If Rakesh sold it for ₹2,537 and made a profit of 18%, then the original cost price (in ₹) of the article for Anju was:

The speed of a boat along and against the current is $22\text{km/hr}$ and $18\text{km/hr}$ respectively. Then the speed of the current (in $\text{km/hr}$) is:

If the selling price is tripled and cost price doubled, the profit would become $65\%$. What is the present profit (in $\%$ )?

By selling a car for $\text{₹}6,400$, Mr. Rao lost $20\%$. Then the cost price of the car is:

Ramanna purchased raw materials for a certain price to manufacture a product. However, owing to shortage of labour, $22.5\%$ of the raw materials could not be utilised and got wasted. $80\%$ of the cost of raw materials used was added as the cost of manufacturing. If Ramanna could sell his product at a price to earn an overall profit of $20\%$ after offering a discount of $20\%$, how many times of the total cost of the raw materials purchased was the marked price of the product?

The price of Petrol increased by $25\%$. In order that expenses on petrol should not increase, one must reduce travel by

A man buys two books for a total of Rs. $410$ and sells both at the exact same price. One gives him a profit of $15\%$ and another a loss of $10\%$. The cost price of both books is

Find the least number of square tiles required to pave the floor of a room $15\text{m }17\text{cm}$ long and $9\text{m }2\text{cm}$ broad.

The ratio of two numbers is $5:6$ and their HCF is $12$. Their LCM is

A $12\text{litre}$ solution of acid and water contains $30\%$ acid. How much water (in litres) must be added to get a solution having $20\%$ acid?

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

In a test, the marks obtained by $\text{E}$ is $30\%$ more than the marks obtained by $\text{F}$. If $\text{F}$ scored $20$ marks, how many marks did $\text{E}$ score?

The average per day income of $A$, $B$ and $C$ is $\text{Rs. }45$. If the average per day income of $A$ and $B$ is $\text{Rs. }40$ and that of $B$ and $C$ is $\text{Rs. }43$, then the per day income of $B$ is:

A person can row $22\frac{1}{2}\text{km}$ an hour in still water and he finds that it takes him twice as long to row up as to row down the stream. The speed of the stream is:

If the speed of a boat moving against the current is $18\text{km/h}$, what is the speed of the stream if the boat's speed downstream is $50\%$ greater than its speed upstream?

$\text{Rs. }6000$ 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:

$A$ started a business with a capital of $\text{Rs. }1,12,000$. After $2$ months, $B$ joined the business with a capital of $\text{Rs. }80,000$, and after another $2$ months, $C$ joined the business with a capital of $\text{Rs. }72,000$. After $10$ months from the start of the business, $B$ withdraws $\text{Rs. }8,000$ and $C$ also withdraws $\text{Rs. }8,000$. If $B$ received $\text{Rs. }9,800$ as his share in the profit at the end of a year, then the total profit was:

A man travels the first $200\text{km}$ of his journey at $80\text{km/h}$. Due to bad weather he travels the next $200\text{km}$ of his journey at $50\text{km/h}$. What is his average speed for the first $400\text{km}$ of his journey?

The average marks of $28$ students in Mathematics was $5$. When $8$ students left the school, the average increased by $0.5$. What is the average of marks obtained by the students who left the school?

A mountaineer ascends $30$ feet at the start of each hour, then pauses to rest and slides back $20$ feet before beginning his climb again at the start of the next hour. If he starts his climb at $8:00\text{a.m.}$, at what time will he first reach a flag positioned $120$ feet above the ground?

The ratio of glycerin and water in a mixture is $3:1$. How much fraction of the mixture must be drawn off and substituted by water so that the ratio of glycerin and water becomes $1:1$?

A container contains two liquids, X and Y, in the ratio $5:3$. When $8\text{liters}$ of the mixture is drawn off, and the container is filled with liquid Y, the ratio of X to Y becomes $2:3$. How many liters of liquid X was in the container initially?

A pump can fill a tank with water in $3\text{hours}$. Due to leakage in the bottom, it takes $3\frac{1}{2}\text{hours}$ to fill it. In what time will the leak empty the fully filled tank?

Kartik walks from point A to B with $50\text{km/hr}$ speed and returns from B to A with a speed of $30\text{km/hr}$. Find his average speed.

By selling a tape-recorder for $\text{Rs. }1900$, I lost $5\%$. What percent shall I gain by selling it for $\text{Rs. }2080$?

Convert $9\text{km/hr}$ into $\text{m/s}$.

The average per day income of A, B and C is $\text{Rs. }45$. If the average per day income of A and B is $\text{Rs. }40$ and that of B and C is $\text{Rs. }43$, then the per day income of B is:

Deepak lent Rs. 8800 to Jaichand for 13 years and Rs. 5500 to Kapil for 12 years on simple interest at the same rate of interest and received Rs. 14432 in all from both of them as interest. The rate of interest per annum is:

A mixture contains alcohol and water in ratio $4:5$. If $10\text{litres}$ of water is added to $27\text{litres}$ of the mixture, find the new ratio of alcohol to water.

Two students appeared for an examination. One of them secured 19 marks more than the other and his marks were 60% of the sum of their marks. The marks obtained by them are:

The strength of a school increases and decreases every alternate year by $15\%$. If it started with an increase in 2012, then the strength of the school in the beginning of 2015, as compared to that in 2012, had (correct to two decimal places):

The average marks of 72 students is shown as 69. It includes a wrong entry of 45 marks instead of 54 marks. The correct average is:

Sowmika and Rachana can complete a piece of work in $40\text{days}$ and $60\text{days}$ respectively. Sowmika starts the work alone, and after $4\text{days}$, Rachana joins her to complete the remaining work. In how many days will the entire work be completed?

Refer to the below data table and answer the following question.
Division / Standard Boys Girls
Division A / Standard 5 20 30
Division B / Standard 5 15 20
Division C / Standard 5 30 10
Division A / Standard 6 30 25
Division B / Standard 6 30 25
Division C / Standard 6 30 20
What is the ratio of total boys to total girls?

₹5,580 is divided among P, Q and R in the ratio of 7:11:13, respectively. What is the difference (in ₹) between the one-third of the largest share and two-fifth of the smallest?

After selling $17$ books for $\text{Rs. }720$, a shopkeeper incurs a loss equal to the cost price (C.P.) of $5$ books. Find the C.P. of a book.

There were two candidates in an election. $10\%$ of voters did not cast their votes. $60$ votes were found invalid. The winning candidate got $47\%$ of the total votes and won by $308$ votes. Find the number of voters enrolled.

Find the value of $(13.49+12.51)\times 13$.

The average of five numbers is 30. If one number is excluded, the average becomes 31. What is the excluded number?

The value of [33{(40×5)+(7×6)}÷11]+(23×15÷24) is:

A merchant sells 195kg of wheat for ₹10,260 at a profit of ₹4.50 per kg of wheat. What is the cost price (in ₹, to the nearest integer) of 15kg of wheat?

If 42÷3+k×3−22÷11+4=28, then the value of k is:

A public library has an average attendance of 410 on Sundays and 230 for the remaining days. The average attendance per day of a month of 30 days beginning with Sunday would be:

The difference between simple interest on a certain sum at the rate of $8\%$ per annum for $18$ months and $24$ months is $\text{Rs }452$. What is the sum (in $\text{Rs}$)?

The bar graph shows the number of SUVs of different brands sold by a dealer in a month. Study the diagram and answer the following question.If the average price of a SUV sold by the dealer is $\text{Rs }8\text{ lakhs}$, then what is the sales (in $\text{Rs lakhs}$) of all the SUVs sold by the dealer in the month?

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: