Question 1

A worker is paid ₹500 per day. If he works for 12 days and completes a job, what is his total wage for the job?

Accepted Answer

Step 1: Total wage = Daily wage × Number of days worked. Step 2: Total wage = ₹500 × 12 = ₹6000. Therefore, the answer is ₹6000.

Question 2

Three workers are paid in the ratio 2:3:5 for a job. If the total payment is ₹10,000, how much does the worker with the highest share receive?

Accepted Answer

Step 1: Total parts = 2 + 3 + 5 = 10. Step 2: The worker with the highest share has 5 parts. Step 3: His payment = (5/10) × ₹10,000 = ₹5,000. Therefore, the answer is ₹5,000.

Question 3

A can do 1/3 of a work in 5 days. In how many days can A complete the entire work?

Accepted Answer

Step 1: A completes 1/3 of work in 5 days. Step 2: To complete full work (3/3), A needs 3 times as many days. Step 3: Total days = 5 × 3 = 15 days.

Question 4

Pipe A can fill a cistern in 12 hours, and Pipe B can empty it in 18 hours. If both pipes are opened simultaneously, how long will it take to fill the cistern?

Accepted Answer

Step 1: Rate of Pipe A (filling) = 1/12 per hour. Step 2: Rate of Pipe B (emptying) = 1/18 per hour. Step 3: Net rate = 1/12 - 1/18 = (3-2)/36 = 1/36 per hour. Step 4: Time to fill = 1 ÷ (1/36) = 36 hours.

Question 5

A's efficiency is 25% more than B's. If A and B together complete a task in 9 days, how many days does B alone need to complete the task?

Accepted Answer

Step 1: Let B's efficiency = 1 unit/day. Then A's efficiency = 1.25 units/day. Step 2: Combined efficiency = 1 + 1.25 = 2.25 units/day. Step 3: Work done in 9 days = 2.25 × 9 = 20.25 units. Step 4: B's time alone = 20.25 ÷ 1 = 20.25 days. Alternatively: Let B's time = x days, A's time = x/1.25 = 0.8x days. Step 5: 1/x + 1/(0.8x) = 1/9. Step 6: (0.8 + 1)/(0.8x) = 1/9 → 1.8/(0.8x) = 1/9 → x = 1.8 × 9 / 0.8 = 20.25 days.

Question 6

Two pipes A and B together can fill a tank in 8 hours. If pipe A alone takes 12 hours more than pipe B alone to fill the tank, how many hours does pipe B take to fill the tank?

Accepted Answer

Step 1: Let B take x hours to fill the tank. Then A takes (x + 12) hours. Step 2: Rate of A = 1/(x+12), Rate of B = 1/x. Step 3: Combined rate = 1/(x+12) + 1/x = 1/8. Step 4: Multiply by 8x(x+12): 8x + 8(x+12) = x(x+12). Step 5: 8x + 8x + 96 = x² + 12x. Step 6: 16x + 96 = x² + 12x. Step 7: x² - 4x - 96 = 0. Step 8: Using quadratic formula or factoring: (x - 12)(x + 8) = 0. Step 9: x = 12 (taking positive value). Therefore, B takes 12 hours.

Question 7

Pipe A fills a tank in 16 hours. Pipe B fills the same tank in 24 hours. If both pipes are opened together, but Pipe A is closed after some time, and Pipe B continues alone and takes a total of 18 hours to fill the tank, for how many hours was Pipe A open?

Accepted Answer

Step 1: Rate of A = 1/16, Rate of B = 1/24 per hour. Step 2: Let Pipe A be open for x hours. Step 3: Work done by A in x hours = x/16. Step 4: Remaining work = 1 - x/16. Step 5: This remaining work is done by B alone in (18 - x) hours. Step 6: So, (18 - x) × (1/24) = 1 - x/16. Step 7: (18 - x)/24 = 1 - x/16. Step 8: Multiply by 48: 2(18 - x) = 48 - 3x. Step 9: 36 - 2x = 48 - 3x. Step 10: x = 12 hours.

Question 8

A team of workers can complete a project in 30 days. After 10 days of work, the team's efficiency increases by 25%. The project is then completed in 12 more days. If the project had been completed at the original efficiency throughout, how many days would it have taken?

Accepted Answer

Step 1: Let original efficiency = e per day. Work done in first 10 days = 10e. Step 2: After 10 days, efficiency becomes 1.25e. Work done in next 12 days = 12 × 1.25e = 15e. Step 3: Total work = 10e + 15e = 25e. Step 4: At original efficiency e, time = 25e / e = 25 days.

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