Question 1

A and B together can complete a piece of work in 12 days. If A's daily wage is ₹500 and B's daily wage is ₹700, and they are paid in the ratio of work done, how much will B receive if the total payment for the completed work is ₹14,400?

Accepted Answer

Step 1: A and B together complete work in 12 days, so combined work rate = 1/12 per day. Step 2: A's daily wage is ₹500 and B's daily wage is ₹700. The ratio of their daily wages = 500:700 = 5:7. Step 3: Since payment is in the ratio of work done, and work done is proportional to daily wage (assuming same number of days worked), B's share = (7/(5+7)) × 14,400 = (7/12) × 14,400 = ₹8,400.

Question 2

A and B together can complete a project in 12 days. A's efficiency is 25% more than B's efficiency. If A and B work together for 8 days and then B leaves, how many more days will A alone take to finish the remaining work?

Accepted Answer

Step 1: Let B's efficiency = x units/day, then A's efficiency = 1.25x units/day. Step 2: Combined efficiency = x + 1.25x = 2.25x units/day. Step 3: Total work = 2.25x × 12 = 27x units. Step 4: Work done in 8 days = 2.25x × 8 = 18x units. Step 5: Remaining work = 27x - 18x = 9x units. Step 6: Time for A to complete remaining work = 9x ÷ 1.25x = 7.2 days. Therefore, answer is 7.2 days or 36/5 days.

Question 3

A, B, and C working together can complete a project in 12 days. A and B together can complete it in 18 days. If A is paid ₹500 per day, B is paid ₹400 per day, and C is paid ₹300 per day, then what is C's share of the total wages if the project is completed in 12 days and wages are distributed in the ratio of work done?

Accepted Answer

Step 1: Find C's work rate. A+B+C complete in 12 days, so combined rate = 1/12 per day. A+B complete in 18 days, so combined rate = 1/18 per day. Therefore, C's rate = 1/12 − 1/18 = (3−2)/36 = 1/36 per day. Step 2: Find individual rates. Let A's rate = a, B's rate = b. We know a + b = 1/18 and daily wages are A:B:C = 500:400:300 = 5:4:3. Since wages are proportional to daily rates (work rate × daily wage = contribution), we have 5a = 4b (from wage ratio). Solving: a = 4k, b = 5k for some k. Then 4k + 5k = 1/18, so k = 1/162. Thus a = 4/162 = 2/81, b = 5/162. Step 3: Verify C's rate = 1/36 = 4.5/162 (consistent). Step 4: Work done by each in 12 days: A does 12 × (2/81) = 24/81 = 8/27. B does 12 × (5/162) = 60/162 = 10/27. C does 12 × (1/36) = 12/36 = 1/3 = 9/27. Total = (8+10+9)/27 = 27/27 ✓. Step 5: Total wages = (500 + 400 + 300) × 12 = 1200 × 12 = ₹14,400. Step 6: C's share = (9/27) × 14,400 = (1/3) × 14,400 = ₹4,800.

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