The ratio of number of boys and number of girls in a school is found to be 15:32 . How many boys and equal number of girls should be added to bring the ratio to 2/3 ?

Option a: 19. Solution: Let the original number of boys and girls in the school be 15k and 32k respectively, where k is a positive integer. Let x be the number of boys and equal number of girls added to the school. The new ratio of boys to girls becomes 2/3 : 15k + x/32k + x = 2/3 To find x in terms of k , we cross-multiply: 3(15k + x) = 2(32k + x) Expand both sides: 45k + 3x = 64k + 2x Subtract 2x and 45k from both sides: x = 64k - 45k x = 19k Since x and k must be positive integers, let us find the smallest positive integer value for x by setting k = 1 : x = 19(1) = 19 This perfectly matches Option A. Hence, Option A is the correct answer.

The ratio of number of boys and number of girls in a school is found to be $15:32$. How many boys and equal number of girls should be added to bring the ratio to $2/3$?

The correct answer is Option a: $19$. Let the original number of boys and girls in the school be $15k$ and $32k$ respectively, where $k$ is a positive integer. Let $x$ be the number of boys and equal number of girls added to the school. The new ratio of boys to girls becomes $2/3$: $$\frac{15k + x}{32k + x} = \frac{2}{3}$$ To find $x$ in terms of $k$, we cross-multiply: $$3(15k + x) = 2(32k + x)$$ Expand both sides: $$45k + 3x = 64k + 2x$$ Subtract $2x$ and $45k$ from both sides: $$x = 64k - 45k$$ $$x = 19k$$ Since $x$ and $k$ must be positive integers, let us find the smallest positive integer value for $x$ by setting $k = 1$: $$x = 19(1) = 19$$ This perfectly matches **Option A**. Hence, **Option A** is the correct answer.

Ratio, Proportion, Indices, LogarithmMCQMTP Sep 24 Series IIQuestion 871 of 305

All Questions

The ratio of number of boys and number of girls in a school is found to be $\displaystyle 15:32$ . How many boys and equal number of girls should be added to bring the ratio to $\displaystyle 2/3$ ?

Options

\displaystyle 19

\displaystyle 27

\displaystyle 23

\displaystyle 20

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Correct Answer

✅ Option a — $\displaystyle 19$

All Options:

A $\displaystyle 19$
B $\displaystyle 27$
C $\displaystyle 23$
D $\displaystyle 20$

Detailed Solution & Explanation

Let the original number of boys and girls in the school be

\displaystyle 15k

and

\displaystyle 32k

respectively, where

\displaystyle k

is a positive integer.
Let

\displaystyle x

be the number of boys and equal number of girls added to the school.
The new ratio of boys to girls becomes

\displaystyle 2/3

\frac{15k + x}{32k + x} = \frac{2}{3}

To find

\displaystyle x

in terms of

\displaystyle k

, we cross-multiply:

3(15k + x) = 2(32k + x)

Expand both sides:

45k + 3x = 64k + 2x

Subtract

\displaystyle 2x

and

\displaystyle 45k

from both sides:

x = 64k - 45k

x = 19k

Since

\displaystyle x

and

\displaystyle k

must be positive integers, let us find the smallest positive integer value for

\displaystyle x

by setting

\displaystyle k = 1

x = 19(1) = 19

This perfectly matches **Option A**.
Hence, **Option A** is the correct answer.

About This Chapter: Ratio, Proportion, Indices, Logarithm

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Ratio, Proportion, Indices, Logarithms

This chapter covers Ratio, Proportion, Indices, Logarithms and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 5-7 Marks weightage. Focus on understanding core concepts rather than memorizing.

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The ratio of number of boys and number of girls in a school is found to be 15:32\displaystyle 15:3215:32. How many boys and equal number of girls should be added to bring the ratio to 2/3\displaystyle 2/32/3?