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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?


A
13
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B
12
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C
10
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D
15
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Solution

The correct option is B 10
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 1Number of days
 12 : x = 4 : 3 ...(ii)

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) or (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.

Mathematics

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