A alone can finish a work in 2 days, while B alone can finish it in 3 days. If they work together to finish it, then out of total wages of Rs. 6000, what will be the 20% of A's share?

Options

A. X 720
B. X 350
C. X 820
D. X 420

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Determine the work done by A and B in one day.
- A can finish the work in 2 days. Therefore, A's work in one day = 1/2 of the work.
- B can finish the work in 3 days. Therefore, B's work in one day = 1/3 of the work.

**Hint:** To find the work done in one day, take the reciprocal of the number of days taken to complete the work.

### Step 2: Calculate the combined work done by A and B in one day.
- Combined work done by A and B in one day = (1/2) + (1/3).
- To add these fractions, find a common denominator, which is 6.
- (1/2) = 3/6
- (1/3) = 2/6
- Therefore, combined work = 3/6 + 2/6 = 5/6 of the work in one day.

**Hint:** When adding fractions, always find a common denominator to combine them.

### Step 3: Determine how many days A and B will take to complete the work together.
- If A and B together can complete 5/6 of the work in one day, then to complete the entire work (1), they will take:
- Days required = 1 / (5/6) = 6/5 days = 1.2 days.

**Hint:** To find the total time taken when working together, divide 1 by the combined work done in one day.

### Step 4: Calculate the efficiency ratio of A and B.
- A's efficiency = 1/2 (work done in one day)
- B's efficiency = 1/3 (work done in one day)
- To find the ratio of their efficiencies, we can express both efficiencies with a common denominator:
- A's efficiency = 3/6
- B's efficiency = 2/6
- The ratio of A's to B's efficiency = 3:2.

**Hint:** Efficiency ratio can be found by comparing the work done by each person in the same unit of time.

### Step 5: Calculate the total wages and A's share.
- Total wages = Rs. 6000.
- The total parts in the efficiency ratio = 3 + 2 = 5.
- A's share = (A's efficiency / Total efficiency) * Total wages = (3/5) * 6000 = Rs. 3600.

**Hint:** To find an individual's share from total wages, multiply the total wages by the fraction of their efficiency over the total efficiency.

### Step 6: Calculate 20% of A's share.
- A's share = Rs. 3600.
- 20% of A's share = (20/100) * 3600 = Rs. 720.

**Hint:** To find a percentage of a value, multiply the value by the percentage (expressed as a fraction).

### Final Answer:
20% of A's share is Rs. 720.

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