A and B can do a piece of work in 25 hours and 30 hours respectively. They began to do the work together but A leaves after some hours and then B completes the remaining work in 18 hours. The number of hours after which A left the work was?

50/11

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80/11

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120/11

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60/11

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Solution

The correct option is E
60/11

(A + B)'s 1 hour's work = $(\frac{1}{25} + \frac{1}{30}) = \frac{11}{150}$

Work done by B in 18 hours = $(\frac{1}{30} \times 18) = \frac{3}{5}$ .
Remaining work = $(1 - \frac{3}{5}) = \frac{2}{5}$

Now, $\frac{11}{150}$ work was done by (A + B) in 1 hour

$\frac{2}{5}$ work done by (A + B) in $(\frac{150}{11} \times \frac{2}{5}) = \frac{60}{11}$ hours

$\therefore \!\,$ A left after $5 \frac{5}{11}$ hours.

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A and B can do a piece of work in 25 hours and 30 hours respectively. They began to do the work together but A leaves after some hours and then B completes the remaining work in 18 hours. The number of hours after which A left the work was?

The correct option is E 60/11 (A + B)'s 1 hour's work = (125+130) = 11150 Work done by B in 18 hours = (130 × 18) = 35. Remaining work = (1−35) = 25 Now, 11150 work was done by (A + B) in 1 hour 25 work done by (A + B) in (15011 × 25) = 6011 hours A left after 5511 hours.