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A can construct a building in 12 days and B can destroy it in 5 days. A worked alone for 7 days and then B joined him for 3 days and left. How many days will A take to complete the building alone after B leaves?

A can construct a building in 12 days and B can destroy it in 5 days. A worked alone for 7 days and then B joined him for 3 days and left. How many days will A take to complete the building alone after B leaves? Correct Answer 46/5 days

GIVEN:

A can construct a building in 12 days and B can destroy it in 5 days.

CONCEPT:

Total work = Time × Efficiency

CALCULATION:

Work done by A in 1 day = 1/12

And

Work done by B in 1 day = -1/5

Now, according to the question:

Work done in 10 days = 7A + 3(A + B)

= 7 × (1/12) + 3 × (1/12 – 1/5)

= 7/12 + 3/12 – 3/5

= 10/12 – 3/5

= 7/30th

Now,

Remaining work = 1 – 7/30 = 23/30th

∴ Number of days in which A will finish the remaining work = (23/30)/(1/12) = 46/5 days

Alternate Method

Suppose total work = 60 units (LCM of 5 and 12)

So,

Efficiency of A = 60/12 = 5

Efficiency of B = 60/5 = -12 (B can distroy the work so efficiency of B is -ive)

Work done in 10 days = 5 × 10 – 12 × 3 = 14 units

So,

Remaining work = 60 – 14 = 46 units

∴ Number of days in which A will finish the remaining work = 46/5 days

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