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A complete $$\frac{7}{{10}}$$ of a work in 15 days, then he completed the remaining work with the help of B in 4 days. In how many day A and B can complete entire work together?
Answer & Solution
Correct Answer:
Option
C
$$\frac{7}{{10}}$$ part of work has been completed by A in 15 days. Then,
Rest work = 1 - $$\frac{7}{{10}}$$ = $$\frac{3}{{10}}$$ part
Given, That $$\frac{3}{{10}}$$ part of the work is completed by A and B together in 4 days. Means,
(A + B) completed the $$\frac{3}{{10}}$$ of work in 4 days
So, (A + B)'s 1 day's work = $$\frac{3}{{10 \times 4}}$$ = $$\frac{3}{{40}}$$
Hence,
(A + B) can complete the work in $$\frac{{40}}{3}$$ = $$13\frac{1}{3}$$ days
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LoginA×7/10=15
A=150/7
Remaining work 1-7/10=3/10
(A+B)3/10=4
A+B =40/3
AS WE KNOW IF THERE IS 7/10 THEN 7 IS COMPLETED WORK AND 10 IS COMPLETE WORK
LCM =COMPLETE WORK
NOW FIND THERE CAPACITY
A = 150/7 LCM IS 10 THATS WHY 10/150/7= 7/15
A= 7/15
A+B = 40/3 LCM IS 10 THEREFORE 10/40/3=3/4
CAPACITY OF A+ B = 3/4
NOW WE FIND CAPACITY OF ONLY B.
SO
B =3/4 -7/15 =17/60
CAPACITY OF A+ B = 7/15+17/60
A+B = 45/60
TOTAL WORK = 10
10/A+B
10/45/60
10×60/45= 40/3
40/3 = 13.33333