Question

A college has 75% of the amount it needs for a new building by receiving an average donation of Rs 600 from the people already solicited. The people already solicited represent 60% of the people the college will ask for the donation. If the college is to raise exactly the amount needed for the new building what should be the average donation from the remaining people to be solicited?
(a) 300
(b) 250
(c) 400
(d) 500

Answer 1

Hint:First, we have to calculate the average donation received from solicited people by assuming the total number of people as y, i.e. 60% of 600y. Then we know that 75% of the total amount has already been solicited. So, we have to find the remaining 25% needed for a new building.

Complete step-by-step answer:
In the given question, first we understand the meaning of the word ‘Solicited’.
Solicited means to ask for or to gain something from someone.
Let us assume that the number of people in college be y. So, on average the donation received for a new building will be Rs. 600 for 60% people.
In mathematical form, it will be written as:
Average donation received from solicited people $=600\times 60\%\text{ of }y$
$=600\times \dfrac{60}{100}\times y$
$=360y$
Now, the remaining people are $\left( 100-60\% \right)=40\%$ of y.
So, as per given in the question, 75% is the total amount collected by 60% of people in college. It is written as
$\therefore 75\%=360y$
So, now we have to find the average number of remaining 40% people.
First, we will find the remaining 25% i.e. $\left( 100-75 \right)\%$ total amount needed for the new building.
$75\%=360y$
$25\%=?$
Now, on using unitary method we will get,
$\therefore \dfrac{25\%\times 360y}{75\%}=120y$
Thus, the total remaining amount for 25% is equal to 120y.
Now, we have to find the average amount needed for this total amount, 120y from 40% of the remaining people in college.
$\therefore \dfrac{120y}{40\%y}=\dfrac{120}{0.4}=300$
Thus, the average amount needed is equal to Rs. 300.
Hence, option (a) is correct.

Note: Students might get confused by this type of tricky question but first they need to identify what all data is given in question. Another way to solve this problem is using direct logic.
Considering a total 100 people in college and direct solving i.e. $60\times 600=36000Rs=\left( 75\% \right)$ amount received by college. So, for remaining 25% will be
$36000=75\%$
$?=25\%$
On solving, we get Rs 12000 which is the total amount of remaining 40 % of people.
So, the average donation by 40 people $=\dfrac{12000}{40}=300$ Rs.