Question

A completes \(\frac{7}{20}\) of a work in 10 days. Then he completes the remaining work with the help of B in 5 days. The time required for A and B together to complete the entire work is :

• A. \(\frac {100}{29}\) days
• B. \(\frac {100}{13}\) days
• C. \(\frac {100}{17}\) days
• D. \(\frac {200}{13}\) days

Answer 1

The Correct Option is B

To solve the problem, let's first determine the amount of work A completes in one day. A completes \(\frac{7}{20}\) of the work in 10 days. Therefore, A's rate of work per day is:

\[\frac{7}{20} \div 10 = \frac{7}{200}\]

This implies A completes \(\frac{7}{200}\) of the work in one day.

In the 10 days, A has completed \(\frac{7}{20}\) of the work. Hence, the remaining work is:

\[1 - \frac{7}{20} = \frac{13}{20}\]

A and B together complete the remaining \(\frac{13}{20}\) of the work in 5 days. Thus, the rate of A and B working together is:

\[\frac{13}{20} \div 5 = \frac{13}{100}\]

The combined rate of A and B is \(\frac{13}{100}\) of the work per day.

To find the time required for A and B together to complete the entire work, we need to find the reciprocal of their rate:

\[\frac{1}{\frac{13}{100}} = \frac{100}{13}\]

Therefore, A and B together can complete the entire work in \(\frac{100}{13}\) days.

Option	Time (days)
a	\(\frac{100}{29}\)
b	\(\frac{100}{13}\)
c	\(\frac{100}{17}\)
d	\(\frac{200}{13}\)

Thus, the correct answer is option b: \(\frac{100}{13}\) days.