Question : P and Q can do a work together in 30 days. Q and R can do the same work together in 24 days and R and P together in 20 days. They started the work together, but Q and R left after 10 days. How many more days will P take to finish the remaining work?
Option 1: 23
Option 2: 21
Option 3: 18
Option 4: 19
Correct Answer: 18
Solution :
LCM of 30, 24 and 20 = 120
Total work = 120 units
Efficiency of (P + Q) = $\frac{120}{30}=4$ units/day
Efficiency of (Q + R) = $\frac{120}{24}=5$ units/day
Efficiency of (R + P) = $\frac{120}{20}=6$ units/day
Now, (P + Q) + (Q + R) + (R + P) = 4 + 5 + 6
⇒ 2 (P + Q + R) = 15
⇒ (P + Q + R) = $\frac{15}{2}$units/day
One day work of (P + Q + R) = $\frac{15}{2}$
Ten day work of (P + Q + R) = $\frac{15}{2}\times10=75$
Remaining work = 120 – 75 = 45
Efficiency of P = efficiency of (P + Q + R) – efficiency of (Q + R) = $\frac{15}{2}-5$ = $\frac{5}{2}$
The remaining work done by P with an efficiency of $\frac{5}{2}$ = $\frac{45}{\frac{5}{2}}$ = 18
Hence, the correct answer is 18.
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