Question

A charitable associate sold an average of 66 raffle tickets per member. Among the female members, the average was 70 raffle tickets. The male to female ratio of the association is 1:2. What was the average number of tickets sold by the male members of the association?
(a) 55
(b) 58
(c) 60
(d) 50

Answer 1

Hint: Let the number of female members be 2x. As the ratio of male to female is 1:2, the number of male is half of the number of females, i.e., half of 2x which is equal to x. Now multiply 2x with 70, to get the total number of tickets sold by females. Also, take the number of tickets sold by each male be y. So, the tickets sold by all the males is xy. So, for finding the average, divide the total tickets sold by the total number of members and equate it with 66 to get the answer.

Complete step-by-step answer:
Let us start the solution to the above question by letting the number of female members be 2x and the number of tickets sold by each member be y.
As the ratio of male to female is 1:2, the number of male is half of the number of females, i.e., half of 2x which is equal to x. Also, it is given that the average of the tickets sold by females is 70, so the number of tickets sold by females:
$\text{Tickets sold by females}=2x\times 70=140x........(i)$
Also, the number of tickets sold by male members is:
$\text{Tickets sold by males}=x\times y=xy........(ii)$
Now we know that the total number of members is the sum of the male and the female members which is equal to 2x+x=3x. Also, the total tickets sold is equal to the sum of tickets sold by male and female members together. So, to find the average, divide the total tickets sold by the total number of members and equate it with 66 to get the answer.
$\dfrac{xy+140x}{2x+x}=66$
$\Rightarrow \dfrac{\left( y+140 \right)x}{3x}=66$
$\Rightarrow y+140=198$
$\Rightarrow y=58$
Therefore, the average number of tickets sold by the male members of the association is 58 tickets. Hence, the answer is option (b).

Note: If you have noticed we let the number of female members as 2x and not x, this is because we know that the number of females is twice the number of males and if we take it to be 2x, we will have to deal with fractions. Also, be very careful about the calculations, as if the calculation goes wrong in any one of the steps, the whole solution turns wrong.