Question

If 40 persons consume 240 kg of rice in 15 days, in how many days will 30 persons consume 48 kg of rice?
(A) 2days
(B) 3days
(C) 4days
(D) 5days

Answer 1

Hint: First of all, find the which factor is directly proportional to the number of days and which factor is inversely proportional to the number of days and by using this we can get the number of days.
Like if the number of days and consumes rice in kg is directly proportional.
Then substitute all the values of kilograms of dal and rice and number of persons into the proportionality formula and solve for the number of days.

Complete step-by-step answer:
Let’s assume,
If 40 persons consume 240 kg rice in 15 days, then 30 persons consume 48 kg rice in x days.
If the number of people increased then the number of days decreased and the number of kg rice consumed increased. The number of days is directly proportional to number of kg consumed rice and inversely proportional to the number of persons.
30 persons consumes rice in kg = R1
40 persons consumes rice in kg = R2
Number of days consuming 240 kg rice = D1\[\]
Number of days consuming 48 kg rice = D2\[\]
So, the value of \[{D_2} = \dfrac{{{R_1} \times 40 \times {D_1}}}{{{R_2} \times 30}}\]
Substituting the values in numerator and denominator, we get
$\Rightarrow$\[{D_2} = \dfrac{{48 \times 40 \times 15}}{{240 \times 30}}\]
Cancel out the factors from numerator and denominator.
$\Rightarrow$\[{D_2} = 4days\]

$\therefore$ 30 persons consume 48 kg of rice in 4 days. Hence, Option (C) is correct.

Note:
Keep in mind that always write the final answer along with the unit.
Another approach is to solve the question is taking constant \[{k_1}\] and \[{k_2}\] .Number of days and number of people are in inverse variation, So constant variation \[{k_1} = \dfrac{{40}}{{30}}\]Number of days and number of kg of rice are in direct variation, So constant variation \[{k_2} = \dfrac{{240}}{{48}}\] Now the value of \[x = \dfrac{{{k_1}}}{{{k_2}}} \times 15\]
\[x = 4days\]