$A$ alone can do a piece of work in $15$ days to that of $B$ alone can do it in $10$ days. If $B$ works at it for $5$ days and then leaves, then $A$ alone can finish the remaining work in _________.

6 \frac{1}{2} d a y s

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7 \frac{1}{2} d a y s

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8 d a y s

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6 d a y s

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Solution

The correct option is A $7 \frac{1}{2} d a y s$
A can do a work in $15$ days
A can do $\frac{1}{15}$ work in $1$ days
B can do a work in $10$ days
B can do $\frac{1}{10}$ work in $1$ day
If B works for $5$ days
$∴$ B does $5 \times \frac{1}{10} = \frac{1}{2}$ work
Remaining work $= 1 - \frac{1}{2} = \frac{1}{2}$
A can do 1 work in 15 days
A can do $\frac{1}{2}$ work in $\frac{15}{2} = 7 \frac{1}{2}$ days.

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A alone can do a piece of work in 15 days to that of B alone can do it in 10 days. If B works at it for 5 days and then leaves, then A alone can finish the remaining work in _________.

The correct option is A 712daysA can do a work in 15 daysA can do 115 work in 1 daysB can do a work in 10 daysB can do 110 work in 1 dayIf B works for 5 days∴ B does 5×110=12 workRemaining work =1−12=12A can do 1 work in 15 daysA can do 12 work in 152=712 days.

$A$ alone can do a piece of work in $15$ days to that of $B$ alone can do it in $10$ days. If $B$ works at it for $5$ days and then leaves, then $A$ alone can finish the remaining work in _________.