Question : A can do $\frac{2}{5}$ of a work in 12 days while B can do $66 \frac{2}{3}\%$ of the same work in 16 days. They work together for 10 days. B alone will complete the remaining work in:
Option 1: 6 days
Option 2: 4 days
Option 3: 8 days
Option 4: 9 days
Correct Answer: 6 days
Solution :
A can do $\frac{2}{5}$ of a work in 12 days.
B can do $66\frac{2}{3}\%$ of the same work in 16 days
They work together for 10 days.
Total work = time × efficiency
A can do whole work in $=12 × (\frac{5}{2})=$ 30 days
$66\frac{2}{3}\% = \frac{200}{3}\% = \frac{2}{3}$
B can do $\frac{2}{3}$ of a work in = 16 days
B can do whole work in $=16 × (\frac{3}{2})=$ 24 days
Let the total work = LCM of 24 and 30 = 120 units
A and B together in 10 days an do (5 + 4) × 10 = 90 units of work
Remaining work = 120 – 90 = 30 units
So, B will complete the remaining work in = $\frac{30}{5}$ = 6 days
Hence, the correct answer is 6 days.
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