[9 days] 12 men or 18 women can reap a field in 14 days. The number of days that 8 men and 16 women will take

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Aptitude

TNPSC G4

10th CBSE Maths

12 men or 18 women can reap a field in 14 days. The number of days that 8 men and 16 women will take to reap it is

5 days

7 days

8 days

9 days

Explanation:
12 men can reap the field in 14 day
⇒ 1 man can reap the field in 12 x 14 = 168 days
⇒ 8 men can reap the field in 168 ÷ 8 = 21 days
⇒ 1 day =1 ÷ 21 = 1/21 of the field
18 women can reap the field in 14 day
⇒ 1 woman can reap the field in 18 x 14 = 252 days
⇒ 16 women can reap the field in 252 ÷ 16 = 15.75 of the field
⇒ 1 day = 1 ÷ 15.75 = 4/63 of the field
So in one day, 12 men and 18 women can reap:
1/21 + 4/63 = 1/9 of the field
Find the number of days needed:
1/9 fo the field = 1 day
9/9 of the field = 1 x 9 = 9 days
Answer: They will take 9 days to reap the field.

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