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Mathematics Practice Questions

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Question 41 · Hard

A man travels 240 km partly by car at 60 km/h and partly by train at 80 km/h. If the total time taken is 3.5 hours, find the distance travelled by car.

Question 42 · Hard

Pipe A can fill a tank in 20 minutes and pipe B in 30 minutes. An outlet C can empty the full tank in 60 minutes. If all three are opened together, how long will the tank take to fill?

Question 43 · Hard

A sum of money amounts to ₹13,310 in 3 years at 10% per annum compound interest, compounded annually. Find the principal.

Question 44 · Hard

An article is sold at a discount of 20% on its marked price and still gives a profit of 28%. If the cost price is ₹1,250, find the marked price.

Question 45 · Hard

A vessel contains 60 litres of a mixture of milk and water in the ratio 7:3. How many litres of water must be added so that the ratio of milk to water becomes 7:5?

Question 46 · Hard

The incomes of A and B are in the ratio 7:9 and their expenditures are in the ratio 5:7. If both save ₹4,000 per month, find B's monthly income.

Question 47 · Hard

A number is first increased by 20%, then decreased by 25%, and finally increased by 10%. If the final value is 990, find the original number.

Question 48 · Hard

The least number which when divided by 16, 24 and 36 leaves remainder 7 in each case is

Question 49 · Hard

A sum amounts to ₹14,520 in 2 years at 10% per annum compound interest. Find the principal.

Question 50 · Hard

A boat covers 36 km downstream in 2 hours and the same distance upstream in 3 hours. Find the speed of the boat in still water.

Question 51 · Hard

The ratio of the radii of two cylinders is 2:3 and their heights are in the ratio 3:4. Find the ratio of their volumes.

Question 52 · Hard

If the roots of 2x²−7x+3=0 are α and β, find the value of α²+β².

Question 53 · Hard

The average of 12 numbers is 46. If the average of the first 7 numbers is 42 and that of the last 6 numbers is 51, find the seventh number.

Question 54 · Hard

A train 180 m long crosses a platform in 18 seconds and crosses a man standing on the platform in 9 seconds. Find the length of the platform.

Question 55 · Hard

A can complete a work in 18 days and B in 24 days. They work together for 6 days. C then joins B, and the remaining work is completed in 4 days. In how many days can C alone complete the work?

Question 56 · Hard

A trader marks an article 50% above its cost price and allows two successive discounts of 10% and 20%. If the cost price is ₹2,400, find the profit percentage.

Question 57 · Hard

A number leaves remainders 5, 8 and 11 when divided by 12, 15 and 18 respectively. Find the least positive number satisfying all three conditions.

Question 58 · Hard

The least number which leaves remainder 7 when divided by 18, 24 and 30 is

Question 59 · Hard

Find the compound interest on ₹25000 at 8% per annum for 2 years.

Question 60 · Hard

A boat travels 72 km downstream in 4 hours and 48 km upstream in 4 hours. Find the speed of the boat in still water.

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