3. Indirect proportion examples
1. If 15 persons can reap a field in 30 days,
in how many days will 21 persons reap the field?
Solution:
We have `M_1=15,D_1=30` and `M_2=21,D_2=x`
`M_1D_1=M_2D_2`
`:. 15 xx 30=21 xx x`
`:. x=(15 xx 30)/(21)`
`:.x=150/7`
2. If 3 persons weave 168 shawls in 14 days,
how many shawls will 8 persons weave in 5 days?
Solution:
We have `M_1=3,D_1=14,W_1=168` and `M_2=8,D_2=5,W_2=x`
`(M_1D_1)/(W_1)=(M_2D_2)/(W_2)`
`:. (3 xx 14)/(168)=(8 xx 5)/(x)`
`:. x=(8 xx 5) xx (168)/(3 xx 14)`
`:.x=160`
3. If 15 persons can fill 35 boxes in 7 days.
How many persons can fill 65 boxes in 5 days?
Solution:
We have `M_1=15,D_1=7,W_1=35` and `M_2=x,D_2=5,W_2=65`
`(M_1D_1)/(W_1)=(M_2D_2)/(W_2)`
`:. (15 xx 7)/(35)=(x xx 5)/(65)`
`:. x=(15 xx 7)/(35) xx (65)/(5)`
`:.x=39`
4. If 15 persons can fill 35 boxes in 7 days.
How many persons can fill 65 boxes in 5 days?
Solution:
We have `M_1=15,D_1=7,W_1=35` and `M_2=x,D_2=5,W_2=65`
`(M_1D_1)/(W_1)=(M_2D_2)/(W_2)`
`:. (15 xx 7)/(35)=(x xx 5)/(65)`
`:. x=(15 xx 7)/(35) xx (65)/(5)`
`:.x=39`
5. If 5 persons working 6 hours a day can reap a field in 20 days,
in how many days will 15 persons reap the field, working 8 hours a day?
Solution:
We have `M_1=5,D_1=20,T_1=6` and `M_2=15,D_2=x,T_2=8`
`M_1D_1T_1=M_2D_2T_2`
`:. 5 xx 20 xx 6=15 xx x xx 8`
`:. x=(5 xx 20 xx 6)/(15 xx 8)`
`:.x=5`
6. If 18 pumps can raise 2170 tonnes of water in 10 days, working 7 hours a day,
in how many days will 16 pumps raise 1736 tonnes, working 9 hours a day?
Solution:
We have `M_1=18,D_1=10,T_1=7,W_1=2170` and `M_2=16,D_2=x,T_2=9,W_2=1736`
`(M_1D_1T_1)/(W_1)=(M_2D_2T_2)/(W_2)`
`:. (18 xx 10 xx 7)/(2170)=(16 xx x xx 9)/(1736)`
`:. x=(18 xx 10 xx 7)/(2170) xx (1736)/(16 xx 9)`
`:.x=7`
This material is intended as a summary. Use your textbook for detail explanation.
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