Question

Rice costing Rs.960 is needed for 16 members for 40 days. What is the cost of rice required for 24 members for 15 days?

Answer 1

Hint: We use the unitary method to find the cost of rice for 1 member for 1 day using the given information. Then again multiply the cost obtained for 1 member per day with the required members for the required number of days.
* Unitary method helps us to find the value of a single unit when we are given the value of multiple units and number of units by dividing value of multiple units by number of units.
* We can find the value of multiple units by multiplying the value of a single unit by number of units.

Complete step by step answer:
We are given the cost of rice which is needed by 16 members for 40 days.
We use the unitary method to find the cost of rice required for 1 member for 40 days.
\[\because \] Cost of rice for 16 members for 40 days \[ = Rs.960\]
\[ \Rightarrow \] Cost of rice for 1 member for 40 days \[ = Rs.\left( {\dfrac{{960}}{{16}}} \right)\]
\[ \Rightarrow \] Cost of rice for 1 member for 40 days \[ = Rs.60\] ………………..… (1)
Now we again apply a unitary method to find the cost of rice for 1 member for 1 day.
From equation (1)
\[\because \] Cost of rice for 1 member for 40 days \[ = Rs.60\]
\[ \Rightarrow \] Cost of rice for 1 member for 1 day \[ = Rs.\left( {\dfrac{{60}}{{40}}} \right)\]
\[ \Rightarrow \] Cost of rice for 1 member for 1 day \[ = Rs.\left( {\dfrac{3}{2}} \right)\] ………………...… (2)
Now we have to find the cost of rice required for 24 members for 15 days.
First we find the cost of rice required for 24 members for 1 day.
So, we use the unitary method and multiply the value obtained for cost from equation (2) by number of members.
\[\because \] Cost of rice for 1 member for 1 day \[ = Rs\left( {\dfrac{3}{2}} \right)\]
\[ \Rightarrow \] Cost of rice for 24 member for 1 day \[ = Rs\left( {\dfrac{3}{2} \times 24} \right)\]
\[ \Rightarrow \] Cost of rice for 24 members for 1 day \[ = Rs36\] ……………..… (3)
Now we use the unitary method and multiply the value obtained for cost from equation (3) by number of days.
\[ \Rightarrow \] Cost of rice for 24 member for 15 days \[ = Rs(36 \times 15)\]
\[ \Rightarrow \] Cost of rice for 24 member for 15 days \[ = Rs540\]

Therefore, the cost of rice required for 24 members for 15 days is Rs.540.

Note:
Students might get confused with two variables given in the question i.e. number of members and number of days. Students are advised to find the value with respect to one variable and then find the value with respect to the second variable; else the solution will be unclear and incorrect.