Question

5 men and 3 boys can together cultivate a 23 acre field in 4 days and 3 men and 2 boys together can cultivate a 7 acre field in 2 days. How many boys will be needed together with 7 men, if they cultivate 45 acre of field in 6 days.

A) 6 B) 4 C) 2 D) 3

Answer 1

Answer:

A) 6 is the answer

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Answer 2

Answer:

Let the area of the land cultivated by 1 boy in 1 day = x acre and by 1 girl = y acre

So (5x + 3y )×4 = 23

=> 20x + 12y =23 ……(1)

(3x + 2y)×2 = 7

=> 6x + 4y = 7 …….(2)

(1) - 3×(3) gives 2x = 2

==> x = 1.

Substituting this in (2) we get

6×1 + 4y = 7

=> y = 1/4

Let n be the number of girls needed together with 7 boys to cultivate 45 acres in 6 days.

Then (7×1 + n× 1/4) 6

= 45

=>42 + 6n/4 =45

=> 6n/4 = 3

=> n = 3×(4/6)= 2

So 2 girls are required.

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