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Byju's Answer
Standard VIII
Mathematics
Inverse Proportion
To feed a fam...
Question
To feed a family of 12 members, 270 kg of rice is required for 30 days. How many members can consume 300 kg of rice in 40 days?
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Solution
Here, the number of members is directly proportional to the number of kgs of rice and inversly proportional to the number of days.
Number of members
Kgs of rice
Number of days
12
270
30
x
300
40
12
:
x
270:300 = 9:10
30:40 = 3:4
Number of members
∝
Kg of rice
⇒
12
:
x
=
9
:
10
.
.
.
(
i
)
Number of members
∝
1
Number of days
⇒
12
:
x
=
4
:
3
.
.
.
(
i
i
)
From (i) and (ii)
12 :
x
=
compound ratio of
9
:
10
and
4
:
3
⇒
12
:
x
=
(
9
:
10
)
×
(
4
:
3
)
⇒
12
:
x
=
(
9
×
4
)
:
(
10
×
3
)
⇒
12
:
x
=
(
36
:
30
)
⇒
12
:
x
=
(
6
:
5
)
∵
Product of means = Product of extremes
⇒
x
×
6
=
12
×
5
⇒
x
=
10
So, 10 members can consume 300 kg of rice in 40 days.
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