A alone can finish a piece of work in 10 days which B alone can finish in 15 days . If they work together and finish it , then out of total wages of Rs. 225 the amount in rupees that A will get .

Answer

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

### Step 1: Determine the work done by A and B
- A can finish the work in 10 days.
- B can finish the work in 15 days.

### Step 2: Calculate the work done per day by A and B
- Work done by A in one day = 1/10 (since A completes the work in 10 days)
- Work done by B in one day = 1/15 (since B completes the work in 15 days)

### Step 3: Calculate the combined work done by A and B in one day
- Combined work done in one day = Work done by A + Work done by B
- Combined work = (1/10) + (1/15)

### Step 4: Find a common denominator to add the fractions
- The least common multiple (LCM) of 10 and 15 is 30.
- Convert the fractions:
- (1/10) = 3/30
- (1/15) = 2/30
- Therefore, Combined work = (3/30) + (2/30) = 5/30 = 1/6

### Step 5: Determine the total work in terms of days
- Since A and B together can complete 1/6 of the work in one day, they will finish the work in 6 days.

### Step 6: Calculate the ratio of work done by A and B
- The ratio of work done by A and B is based on their efficiencies:
- Efficiency of A = 1/10
- Efficiency of B = 1/15
- The ratio of their efficiencies is:
- Efficiency of A : Efficiency of B = (1/10) : (1/15)
- This simplifies to 3:2 (after finding a common denominator).

### Step 7: Calculate the total parts of the ratio
- Total parts = 3 + 2 = 5

### Step 8: Calculate A's share of the wages
- Total wages = Rs. 225
- A's share = (A's part / Total parts) * Total wages
- A's share = (3/5) * 225 = 135

### Final Answer
- The amount that A will get is Rs. 135.

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