Question

If Rama can do a piece of work in 'a' days and Vimal can do it in a+16 days, and they finish it together in 15 days, find 'a'.

A. a=10
B. a=15
C. a=20
D. a=25

Answer 1

To find 'a', we set up an equation based on the combined work rate of Rama and Vimal. Solving this equation yields 'a' equals 15 days, so Rama can complete the work in 15 days by himself, corresponding to option B.

Step-by-step explanation:

The question concerns solving an equation based on the combined work rate of Rama and Vimal. Rama can complete a job in 'a' days, while Vimal can complete it in 'a+16' days. Together, they finish the same job in 15 days.

Let's denote the part of the job that each person can complete per day as their work rate. Rama's work rate is 1/a, and Vimal's work rate is 1/(a+16). Together, their combined work rate is the sum of their individual work rates, which equals the reciprocal of the time they take to finish the job together, 1/15.

As a formula, we have:

1/a + 1/(a+16) = 1/15

By solving this equation for 'a', we can determine Rama's work rate independently. Doing this yields:

a2 + 16a = 15a + 240

a2 + a - 240 = 0

Factoring this quadratic equation, we find:

(a + 16)(a - 15) = 0

Thus, either a = -16 which is not possible since time cannot be negative, or a = 15.

Therefore, Rama can do the work by himself in 15 days, which corresponds to option B.