Question

A piece of work can be done by Ram in 10 days. If Mohan joined him and both together finished the work in 6 days, then the ratio of their one day work is:

• A. 1:3
• B. 2:3
• C. 3:2
• D. 3:1

Hint:

When two people work together, their combined work rate is the sum of their individual rates.

Answer 1

The Correct Option is C

Let the amount of work done by Ram in one day be \( R \), and by Mohan in one day be \( M \). We are told that Ram can complete the work in 10 days, so \( R = \frac{1}{10} \) (since work is done in one day). When Mohan joins, both complete the work in 6 days, so: \[ R + M = \frac{1}{6}. \] Substituting \( R = \frac{1}{10} \) into the equation: \[ \frac{1}{10} + M = \frac{1}{6} \quad \Rightarrow \quad M = \frac{1}{6} - \frac{1}{10} = \frac{5 - 3}{30} = \frac{2}{30} = \frac{1}{15}. \] Thus, Mohan does \( M = \frac{1}{15} \) of the work in one day. Now, the ratio of their one day work is: \[ \frac{R}{M} = \frac{\frac{1}{10}}{\frac{1}{15}} = \frac{15}{10} = 3:2. \] Thus, the ratio of their one day work is 3:2, which corresponds to option (3).