Maths-
General
Easy

Question

A, B and C can reap a field in 15 ¾ days; B, C and D in 14 days; C, D and A in 18 days; D, A and B in 21 days. In what time can A, B, C and D together reap it?

Hint:

Hint:
When two quantities of different units are compared and expressed as a ratio, it is known as Rate. For example, a car travels at a speed of 100 kilometres per hour, then it means in one hour it covers 100 kilometres.

The correct answer is: 12 3/5 days


    Let’s say the total work done to reap the field is represented as W and let’s say the work done by A in 1 day is WA, work done by B in 1 day is WB,work done by C in 1 day is WC and work done by D in 1 day is WD
    Step 1 of 3:
    It is given that A, B and C can reap a field in 15 ¾ days or 15.75 days. So we can write
    WA cross times 15.75 + WB cross times 15.75 + WC cross times 15.75 = W
    WA  + WB + WC = fraction numerator w over denominator 15.75 end fraction …….(1)
    It is given that  B, C and D can reap a field in 14 days. So we can write
    WB cross times 14 + WC cross times 14 + WD cross times 14 = W
    WB + WC + WD = w over 14…….(2)
    It is given that  C, D and A can reap a field in 18 days. So we can write
    WC cross times 18 + WD cross times 18 + WA cross times 18 = W
    WC + WD + WA = w over 18…….(3)
    It is given that  D, A and B can reap a field in 21 days. So we can write
    WC cross times 21 + WD cross times 21 + WA cross times 21 = W
    WD + WA + WB = w over 21…….(4)
    Step 2 of 3:
    Now, adding equations (1), (2), (3) and (4)
    3(WA  + WB + WC + WD) = fraction numerator W over denominator 15.75 end fraction plus W over 14 plus W over 18 plus W over 21
    WA  + WB + WC + WD = fraction numerator 5 w over denominator 63 end fraction……(4)
    Step 3 of 3:
    Let’s say the time taken by all of them to complete the work is t. So we can write
    WA cross times t + WB cross times t + WC cross times t + WD cross times t = W
    t(WA  + WB + WC + WD) = W
    Using equation (4)
    t cross timesfraction numerator 5 w over denominator 63 end fraction = W
    t = 63 over 5 days = 123 over 5 days.
    Final Answer:
    Hence, the time taken by A, B, C and D together to reap the field is 12 3 over 5 days.

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