Question

P completes \( \frac{13}{20} \) of a work in 9 days. Then he completes the remaining work with the help of Q in 4 days. The time required for P and Q together to complete the entire work is:

• A. \(11\frac{2}{7}\) days
• B. \(11\frac{3}{7}\) days
• C. \(12\frac{4}{7}\) days
• D. \(12\frac{5}{7}\) days

Hint:

When two people work together, add their rates of work. Here, P's rate is combined with Q's rate to determine the total time.

Answer 1

The Correct Option is B

Step 1: Work done by P in 9 days. \[ \text{Work completed by P in 9 days} = \frac{13}{20} \quad \Rightarrow \quad \text{Work completed by P in 1 day} = \frac{13}{20} \div 9 = \frac{13}{180}. \] Step 2: Remaining work after P's 9 days of work. \[ \text{Remaining work} = 1 - \frac{13}{20} = \frac{7}{20}. \] Step 3: Work done by P and Q together in 4 days. \[ \text{Work completed by P and Q together in 4 days} = \frac{7}{20} \quad \Rightarrow \quad \text{Work done by P and Q together in 1 day} = \frac{7}{20} \div 4 = \frac{7}{80}. \] Step 4: Time taken for P and Q to complete the entire work. Since the combined rate of P and Q is \( \frac{7}{80} \) work per day, the time taken to complete the entire work is: \[ \text{Total time} = \frac{1}{\frac{7}{80}} = \frac{80}{7} = 11 \frac{3}{7} \text{ days}. \]