Question

A,B and C can reap a field in 63/4 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?

Answer 1

Here is the answer of your asked problem

Answer 2

Given:

Time taken to reap the field are as follows:

A, B & C in $\frac{63}{4}$ days

B, C & D in 14 days

C, D & A in 18 days

D, A & B in 21 days

To find:

Time taken by A, B, C & D  together to reap the field

Solution:

The amount of work done in reaping the field 1 day is:

A + B + C → $\frac{4}{63}$

B + C + D → $\frac{1}{14}$

C + D + A → $\frac{1}{18}$

D + A + B → $\frac{1}{21}$

Now,

The amount of work done by A, B, C & D together in 1 day will be:

[A + B + C] + [B + C + D] + [C + D + A] + [D + A + B] = $\frac{4}{63}\:+\:\frac{1}{14}\:+\:\frac{1}{18}\:+\:\frac{1}{21}$

⇒ [3A + 3B + 3C + 3D] = $\frac{8\:+\:9\:+\:7\:+\:6}{126}$

⇒ 3 [A + B + C + D] = $\frac{30}{126}$

⇒ [A + B + C + D] = $\frac{30}{126}$ × $\frac{1}{3}$

⇒ [A + B + C + D] = $\frac{10}{126}$

⇒ [A + B + C + D] = $\frac{5}{63}$

Thus,  $\boxed{The\: time\: taken\: by\: A\:, B, C \:and\: D\: together\: to\: reap\: the\: field\: is\:\frac{63}{5}\: days\: or\:12.6\:days. }$

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