Question

A can do a work in 10 days and B can do it in 15 days. They worked together for 4 days and then A left the work. In how many days can B finish the remaining work? If the remuneration of the work is one thousand rupees, how much amount would each person get?

Answer 1

Answer:

A( 10 )

B(15)

total unit of work = 30

for 1 day,

A = 3*4 = 12

B = 2

so,

remaining work = 30-12 = 18

B = 2 unit = 1day

= 1 unit = 1/2day

= 18 unit = 18/2

= 9 days

so,

1 day = 1000

9 days = 9*1000= 9000rup

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Answer 2

Correct Question: A can do a work in 10 days and B can do it in 15 days. They worked together for 4 days and then A left the work. In how many days can B finish the remaining work? If the remuneration of the work is one thousand rupees per day, how much amount would each person get?

Given: Number of days taken by A to do the work alone = 10 days

           Number of days taken by B to do the work alone = 15 days

           Number of days A and B worked together = 4 days

To find: The number of days B takes to finish the remaining work after A leaves and their remunerations

Solution: According to the given question,

Time taken by A to finish the work = 10 days

Time taken by B to finish the work = 15 days

Work done by A in 1 day = $\frac{1}{10}$

Work done by B in 1 day = $\frac{1}{15}$

Work done by A and B together in 1 day = $\frac{1}{10} + \frac{1}{15} = \frac{3 \ + \ 2}{30} = \frac{5}{30} = \frac{1}{6}$

Work done by them together in 4 days = $4*\frac{1}{6}$ = $\frac{4}{6}$

The remaining work = $(1-\frac{4}{6})$ i.e., $\frac{2}{6}$   (to be done by B alone)

Now,  $\frac{1}{15}$ work is done by B in 1 day

∴  $\frac{2}{6}$  work will be done by him in $(\frac{2}{6} * 15 )$ days = 5 days

Thus, B takes 5 days to finish the remaining work.

Now, given that remuneration of the work is Rs. 1,000 per day

Number of days A worked = 4

Number of days B worked = 4 + 5 = 9

∴ A's remuneration = $4*1,000 = Rs. \ 4,000$

∴ B's remuneration = $9*1,000 = Rs. \ 9,000$

Hence, B finishes the remaining work in 5 days and gets Rs. 9,000 as remuneration and A's remuneration is Rs. 4,000.