Two men with weights in the ratio 4:3 run up a staircase in time in the ratio 12:11. The ratio of power of the first to that of second is

Options

A. `4/3`
B. `12/11`
C. `48/33`
D. `11/9`

Answer

To solve the problem, we need to find the ratio of power of the first man to that of the second man. Let's break it down step by step.

### Step 1: Understand the given ratios
We have two men with weights in the ratio of 4:3, and they run up a staircase in a time ratio of 12:11.

Let:
- Weight of the first man (m1) = 4x
- Weight of the second man (m2) = 3x
- Time taken by the first man (t1) = 12y
- Time taken by the second man (t2) = 11y

### Step 2: Determine the work done by each man
The work done (W) in running up the staircase can be expressed as:
\[ W = \text{Weight} \times \text{Height} \]
Assuming the height of the staircase is h, we can write:
- Work done by the first man (W1) = m1 * h = 4x * h
- Work done by the second man (W2) = m2 * h = 3x * h

### Step 3: Calculate the power for each man
Power (P) is defined as work done per unit time:
\[ P = \frac{W}{t} \]
Thus, we can express the power for each man:
- Power of the first man (P1):
\[ P1 = \frac{W1}{t1} = \frac{4xh}{12y} = \frac{4xh}{12y} = \frac{xh}{3y} \]

- Power of the second man (P2):
\[ P2 = \frac{W2}{t2} = \frac{3xh}{11y} = \frac{3xh}{11y} \]

### Step 4: Find the ratio of the powers
Now, we can find the ratio of the powers of the first man to the second man:
\[ \frac{P1}{P2} = \frac{\frac{xh}{3y}}{\frac{3xh}{11y}} \]

### Step 5: Simplify the ratio
When we simplify the ratio:
\[ \frac{P1}{P2} = \frac{xh}{3y} \times \frac{11y}{3xh} = \frac{11}{9} \]

### Final Answer
Thus, the ratio of power of the first man to that of the second man is:
\[ \frac{P1}{P2} = \frac{11}{9} \]