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
• B. 12
• C. 10
• D. 15

Answer 1

The correct option is C 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 $\propto$ Kg of rice
$\Rightarrow 12:x=9:10...\left(i\right)$

$Numberofmembers\propto \frac{1}{Numberofdays}$
$\Rightarrow 12:x=4:3...\left(ii\right)$

From (i) and (ii)
12 : $x$
$=\text{compound ratio of}9:10\text{and}4:3$
$\Rightarrow 12:x=(9:10)\times (4:3)$
$\Rightarrow 12:x=(9\times 4):(10\times 3)$
$\Rightarrow 12:x=(36:30)or(6:5)$

$\because$ Product of means = Product of extremes
$\Rightarrow x\times 6=12\times 5$
$\Rightarrow x=10$

So, 10 members can consume 300 kg of rice in 40 days.