Two men with weights in the ratio 5 : 3 run up a staircase in times in the ratio 11 : 9. The ratio of power of first to that of second is

The correct option is 15/11.

To find the ratio of the power of the two men, we can break down the problem using the physical definition of power.

Step 1: Understand the formula for power
Power ($P$) is defined as the rate at which work is done:
$P=\frac{\text{Work Done}}{\text{Time Taken}}$
When a person of weight $F$ climbs a staircase of vertical height $h$, the work done against gravity is:
$\text{Work Done}=F·h$
Therefore, the power exerted is:
$P=\frac{F·h}{t}$

Step 2: Identify the given ratios
Both men run up the same staircase, which means the vertical height ($h$) is constant for both.
Let the weights of the first and second men be $F_1$ and $F_2$ respectively. The ratio of their weights is:
$\frac{F_1}{F_2}=\frac{5}{3}$
Let the times taken by the first and second men be $t_1$ and $t_2$ respectively. The ratio of their times is:
$\frac{t_1}{t_2}=\frac{11}{9}$

Step 3: Calculate the ratio of their powers
The ratio of the power of the first man ($P_1$) to that of the second man ($P_2$) is given by:
$\frac{P_1}{P_2}=\frac{\left(\frac{F_1·h}{t_1}\right)}{\left(\frac{F_2·h}{t_2}\right)}$
Since $h$ is the same in both the numerator and denominator, we can simplify this to:
$\frac{P_1}{P_2}=\left(\frac{F_1}{F_2}\right)·\left(\frac{t_2}{t_1}\right)$
Substituting the given ratios into the equation:
$\frac{P_1}{P_2}=\left(\frac{5}{3}\right)·\left(\frac{9}{11}\right)$
Simplifying the fractions:

Thus, the ratio of the power of the first man to that of the second man is 15/11.