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If A and B can together earn Rs. 540 in 6 days, B and C can together earn Rs. 420 in 5 days and A and C can together earn Rs. 644 in 7 days then in how many days can A, B and C working together earns Rs. 532?

If A and B can together earn Rs. 540 in 6 days, B and C can together earn Rs. 420 in 5 days and A and C can together earn Rs. 644 in 7 days then in how many days can A, B and C working together earns Rs. 532? Correct Answer 4

A and B can together earn Rs. 540 in 6 days

⇒ A and B ‘s 1 day earning = 540/6 = Rs. 90      ----(1)

B and C can together earn Rs. 420 in 5 days

⇒ B and C‘s 1 day earning = 420/5 = Rs. 84       ----(2)

A and C can together earn Rs. 644 in 7 days

⇒ A and C’s 1 day earning = 644/7 = Rs. 92       ----(3)

Let the required no. of days be n then A + B + C can earn 532/n in 1 day.       ----(4)

From (1) and (4),

C’s 1 day earning = 532/n - 90

From (2) and (4),

A’s 1 day earning = 532/n - 84

⇒ A and C’s 1 day earning = 532/n - 90 + 532/n - 84 = 1064/n - 174      ----(5)

From (3) and (5),

1064/n - 174 = 92

⇒ n = 1064/266

⇒ n = 4

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