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Answer:
Given :-
A 10 hectare field is reaped by 2 men, 3 women and 4 children in 10 days. If a man, a woman and a child work in the ratio 5:4:2
To Find :-
A 16 hectare field will be reaped by 6 men, 4 women and 7 children in:
Solution :-
Ratio = 5:4:2
Finding all people work in one day
For men
Work of men in one day = Men in ratio × Given men in 10 hectare
Work of men in one day = 5 × 2
Work of men in one day = 10
For women
Work of women in one day = Women in ratio × Given Women in 10 hectare
Work of women in one day = 4 × 3
Work of women in one day = 12
For children
Work of children in one day = Children in ratio × Given Children in 10 hectare
Work of children in one day = 2 × 4
Work of children in one day = 8
Now
(Men + Women + Children) × Time/Field reaped
(10 + 12 + 8) × 10/10
30 × 10/10
300/10
Let the time be t
For men
Work of men in one day = Men in ratio × Given men in 16 hectare
Work of men in one day = 5 × 6
Work of men in one day = 30
For women
Work of women in one day = Women in ratio × Given Women in 16 hectare
Work of women in one day = 4 × 4
Work of women in one day = 16
For children
Work of children in one day = Children in ratio × Given Children in 16 hectare
Work of children in one day = 2 × 7
Work of children in one day = 14
By using same formula
(Men + Women + Children) × Time/Field reaped
(30 + 16 + 14) × T/16
60T/16
Comparing both
300/10 = 60T/16
300 × 16/10 × 60 = T
5 × 16/10 = T
80/10 = T
8 = T
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