Question

$\small \tt \leadsto \red{Q} \purple{u} \green{ e} \blue{s} \red{t} \purple{i} \green{o} \blue{n}$
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, a 16 hectare field will be reaped by 6 men, 4 women and 7 children in:

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Answer 1

$\sf\small\underline\green{Given:-}$

$\tt{\leadsto (2m+3w+4c)=10days}$

$\tt{\leadsto (6m+4w+7c)=?days}$

$\sf{\leadsto Field\:reaped\:_{(2m+3w+4c)}=10hectare}$

$\sf{\leadsto Field\:reaped\:_{(6m+4w+7c)}=16hectare}$

$\sf{\leadsto Ratio\:_{(for\:both)}=5:4:2}$

$\sf\small\underline\green{To\:Find:-}$

$\tt{\leadsto Work\:done\:_{(6m+4w+7c)}=?days}$

$\sf\small\underline\green{Solution:-}$

To solve this question we have to use direct or indirect variations to compare between two conditions. As per the given clue .

$\sf\small\underline\green{Calculation\: begin:-}$

• As per the first case - ( i ) :-

$\tt{\leadsto \dfrac{[2m(5) + 3w(4)+4c(2)]*days}{field\:reaped}}$

$\tt{\leadsto \dfrac{(10+12+8)*10}{10}}$

$\tt{\leadsto \dfrac{300}{10}}$

• As per the 2nd case - ( ii ) :-

$\tt{\leadsto \dfrac{[6m(5) + 4w(4)+7c(2)]*days}{field\:reaped}}$

$\tt{\leadsto \dfrac{(30+16+14)*D}{16}}$

$\tt{\leadsto \dfrac{60*D}{16}}$

• Comparing with case (I) and (ii) :-

$\tt{\leadsto Case-(i)=Case-(ii)}$

$\tt{\leadsto \dfrac{300}{10}=\dfrac{60D}{16}}$

$\tt{\leadsto 60D*10=300*16}$

$\tt{\leadsto 600D=4800}$

$\tt{\leadsto 6D=48}$

$\tt{\leadsto D=8}$

$\sf\large{Hence,}$

$\tt{\leadsto Work\:done\:_{(6m+4w+7c)}=8\:days}$

Answer 2

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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