2. If 2 men and 3 boys can do a piece of work in 8 days, while
3 men and 2 boys can do it in 7 days, how long will 5 men
200
and 4 boys take to do it?
(a) 2 days
(c) 4 days
(b) 3 days
(d) 5 days
Answers
Answer:
(c) 4 days
Step-by-step explanation:
Given,
2 men and 3 boys can do a work in 8 days and
3 men and 2 boys can do it in 7 days
In one day work,
The given information can be written as
2 men + 3 boys = 1/8 ------->(1)
3 men + 2 boys = 1/7 ------->(2)
(2) * 3 ==> 9 men + 6 boys = 3/7 ------>(3)
(1) * 2 ==> 4 men + 6 boys = 2/8 ------>(4)
(3) - (4) ==> 5 men = 3/7 - 1/4
= (3*4 - 1*7) / 28
= (12 - 7) / 28
==> 5 men = 5/28 ------------->(5)
(1) * 3 ==> 6 men + 9 boys = 3/8 --------->(6)
(2) * 2 ==> 6 men + 4 boys = 2/7 --------->(7)
(6) - (7) ==> 5 boys = 3/8 - 2/7
= (3*7 - 2*8) / 56
= (21 - 16) / 56
==> 5 boys = 5/56
==> 1 boy = 1/56
==> 4 boys = 4/56 -------------->(8)
To find:
5 men and 4 boys [ (5) + (8)]
==> 5 men + 4 boys = 5/28 + 4/56
= 5/28 + 2/28
= 7/28
==> 5 men + 4 boys = 1/4 [ Since it is in 1 day work]
Therefore, 5 men and 4 boys can do the work in 4 days.
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