Question

The ratio of the number of boys and girls in a college is 7:8. If the percentage increase in the number of boys and girls be 20% and 10% respectively what will be the new ratio:
A. 8:9
B. 17:18
C. 21:22
D. Cannot be determined

Answer 1

Hint: As the ratio is given as 7:8. So, we can say the number of boys to that of girls is 7x, 8x respectively. Then, find the new number of boys and girls using formula if d is value of percent of increase is,
\[{\rm{New \space value = Original \space value + }}\dfrac{d}{{100}} \times {\rm{original \space value}}\]

Complete step-by-step answer:
In a college, the ratio of number of boys to number of girls is given which is 7:8. Now, we are further told that there is an increase in the number of boys by 20% and in the number of girls by 10%. So, after the increase what will be the new ratio between boys and girls, we have to find out.
Now, as we are given the ratio of boys to that of girls is 7:8. So, we can say that, number of boys and girls are 7x and 8x respectively.
Now, we are told that the number of boys has increased by 20%. We will find it in terms of x by using the formula, if an original value is increased by p%, then, its new value we can find out by,
\[{\rm{New \space value = Original \space value + }}\dfrac{P}{{100}} \times {\rm{original \space value}}\]
So, here numbers of boys originally were 7x and there is an increase of 20%. So, we can find out the new value of number of boys by using formula,
\[\begin{array}{l}{\rm{New \space value = Original \space value + }}\dfrac{P}{{100}} \times {\rm{original \space value}}\\ \Rightarrow {\rm{ New \space value = }}7x + \dfrac{{20}}{{100}} \times 7x\\ \Rightarrow {\rm{ New \space value = }}7x + 1.4x = 8.4x\end{array}\]
Hence, we can say that, new value for the number of boys is 8.4x.
Now, we will apply this for the number of girls too, which are originally 8x in number. So, by using the formula,
\[{\rm{New \space value = Original \space value + }}\dfrac{P}{{100}} \times {\rm{original \space value}}\]
Hence, original value is 8x and p is 10, so we get,
\[\begin{array}{l}{\rm{New \space value = }}8x + \dfrac{{10}}{{100}} \times 8x\\ \Rightarrow {\rm{New \space value = }}8x + 0.8x\\ \Rightarrow {\rm{New \space value = }}8.8x\end{array}\]
Hence, we can say that, new value for the number of girls is 8.8x.
So, we can say that the new ratio of boys to girls will be $8.4x : 8.8x$ or 21 : 22.
So, the correct option is C.

Note: If instead of increase percentage, there is a decrease percent, let’s say d%. So, we can find new value by using formula,
\[{\rm{New \space value = Original \space value - }}\dfrac{d}{{100}} \times {\rm{original \space value}}\]
We have to take the respective ratios and increase in percentages from the question carefully. We should not make the mistake of taking the ratio of boys:girls as 8:7, this can change the full solution.