Time and Work [समय और काम]-03

Question: To do a certain work B would take three times as long as A and C together and C twice as long as A and B together. The three men together complete the work in 10 days. How long would A take to complete the work alone?  [Ans. (c) 24 days]

(a) 25 days  (b) 30 days  (c) 24 days   (d) 40 days   (e) None of these

Solution:

Detailed Explanation: Given that, to do a certain work B would take three times as long as A and C together. So, 3B=A+C.

So, A+B+C= (A+C) +B=3B+B=4B

Given that the three men A, B and C together can complete the whole work in 10 days. So, 4B can complete the work is 10 days. Therefore, B alone can complete the entire work is 40 days.

Also, since C takes twice the time than that of A and B together. So, 2C=A+B

So, (A+B)+C=2C+C=3C

Thus, 3C can complete the work is 10 days. Therefore, C alone can complete the entire work is 30 days.

Since the three men A, B and C together can complete the whole work in 10 days.

Therefore, A’s one day work = [(1/10) – {(1/40) + (1/30)}] = 1/24

So, A alone can do the work is 24 days. Ans.

                                                               Solution:

                                                       3B=A+C and 2C=A+B

                                             A+B+C=4B ≡10 days, so B≡40 days                                             

                                             A+B+C=3C ≡10 days, so C≡30 days                                                                  

                                                      A=  – [  + ] = ,

                                                So, A=24 days Ans.