Question

The ratio of the number of student studying in schools A, B and C is 6 : 8 : 7 respectively if the number of student studying in each of the schools is increased by 20%, 15% and 20% respectively then what will be the new ratio of the number of student in school A, B and C?
(a) 18 : 23 : 21
(b) 16 : 28 : 30
(c) 20 : 12 : 36
(d) 22 : 21 : 12

Answer 1

Hint: Suppose the number of students in schools A, B and C as $6x,8x$ and $7x$ respectively. Now, increase these values by 20%, 15% and 20% respectively to get the new number of students belong to the respective schools. And hence, calculate the ratio among them now, and eliminate $x$ to get the ratio in simplified form.

Complete step-by-step solution -
Let us suppose the number of students studying in schools A, B and C is $6x,8x$ and $7x$ respectively as the ratio of the number of students are given as 6: 8: 7.
So, we get
Number of students in school A = $6x$
Number of students in school B = \[8x\]
Number of students in school C = $7x$
Now, as the number of students studying in each of the schools have increased by 20%, 15% and 20% respectively (A, B and C).
So, we can calculate the increased number of students by adding the previous number of students to the giving percentage increase in them.
So, we know the relation for calculating $x%$ of $y$ as
$=\dfrac{x\times y}{100}.........\left( i \right)$
So, we can get the total number of students in school A as
Total number of students in school A = 6x+20% of 6x
So, using the relation (i) we get the above expression as
$\begin{align}
  & =6x+\dfrac{20}{100}\times 6x \\
 & =6x+\dfrac{6x}{5}=\dfrac{30x+6x}{5}=\dfrac{36x}{5} \\
\end{align}$
Hence, we get
Total students in school A after increment by 20% = $\dfrac{36x}{5}$
Similarly, we can calculate total number of students in school B after increasing by 15% as
$\begin{align}
  & =8x+8x\times \dfrac{15}{100} \\
 & =8x+8x\times \dfrac{3}{20}=8x+\dfrac{2x\times 3}{5} \\
 & =\dfrac{40x+6x}{5}=\dfrac{46x}{5} \\
\end{align}$
Hence, we get
Total number of students in school B after increment by 15% as
$=\dfrac{46x}{5}$
Similarly, we can get total number of students in school C after increasing by 20% as
$\begin{align}
  & =7x+7x\times \dfrac{20}{100} \\
 & =7x+7x\times \dfrac{1}{5}=7x+\dfrac{7x}{5} \\
 & =\dfrac{35x+7x}{5}=\dfrac{42x}{5} \\
\end{align}$
Hence, we get
Total number of students in school C after increasing the strength of students by 20% as
$=\dfrac{42x}{5}$
Hence, the new ratio of number of students in school A, B and C are given as
$\dfrac{36x}{5}:\dfrac{46x}{5}:\dfrac{42x}{5}$
Multiply the above relation by 5 to each fraction, we get
$36x:46x:42x$
Divide the whole relation by $2x$, we get
$18:23:21$
Hence the new ratio will be $18:23:21$
So, option(a) is correct.

Note: Another approach for the question would be that we can suppose the number of students in school A, B, C as $x,y,z$ as well (three different variable) and increase them by 20%, 15% and 20% respectively and hence, get the ratio by using the ratio $x:y:z$ as $6:8:7$ .So, it can be another approach as well. But the approach in the solution is better as it involves only one variable. One may get confused with the ratio of three terms as we generally are familiar with the ratio of two terms only. So, one may take the ratios given in three terms in the ratio of two terms by splitting them i.e. ratio 6: 8: 7can be understandable as 6: 8 and 8: 7 and 6: 7 between the given quantities. So, don’t confuse it with the ratio of three terms. Just try to relate it as the same as the ratio of two terms.