# Moderate Ratios & Proportion Solved QuestionAptitude Discussion

 Q. There is certain numbers of toys in the box. They are divided into such a way that the person who gets  (dfrac{1}{4}) of the whole gets thrice of what the others get on an average. Find the number of people amongst whom the toys are distributed?
 ✖ A. 8 ✔ B. 10 ✖ C. 12 ✖ D. 9

Solution:
Option(B) is correct

If the person who gets $\dfrac{1}{4}$ of the whole gets thrice of what the others get on an average, each one will get = $\dfrac{1}{3}\times \dfrac{1}{4}=\dfrac{1}{12}$ of the whole.

Therefore, if there are $k$ persons other than the person who gets one-fourth, then

\begin{align*} \dfrac{1}{4}+\dfrac{k}{12}&=1\\ k&=9 \end{align*}

Hence, total number of people = 10.

## (4) Comment(s)

Ira
()

1/4= 3* (3/4)*(1/(x-1))

The above equation (from Naga's answer) has been derived like this:

The statement says that 1/4 equals 3 times 'the average'.

The average = (Toys that the remaining men get/No. of remaining men).

= (3/4) / (x-1)

= (3/4) * (1/x-1)

Now putting this average back to the statement 1:

= 1/4 = 3* (3/4) * (1/x-1)

Solving this, we get x = 10

Naga
()

you get the same answer with another approach!!!!

lets assume we have 1 toy and x men.

then out of x men, 1 gets 1/4 th of the toy. hence the remaining 3/4th is to be distributed among x-1 men.

according to the given statement,

1/4= 3* (3/4)*(1/(x-1))

=> (x-1)/4 = 9/4

=>x-1=9

=>x=10.

Navjot Kaur
()