If x:y = 2:3 , then (5x+2y):(3x-y) =

Option b: 16:3. Solution: To determine the ratio (5x+2y):(3x-y) , we first use the given information about the ratio of x to y . Given that x:y = 2:3 . This can be expressed as a fraction: x/y = 2/3 From this relationship, we can introduce a common non-zero constant, say k , such that: x = 2k y = 3k Since x:y = 2:3 , neither x nor y can be zero, which implies that k ≠ 0 . Now, we substitute these expressions for x and y into the ratio we need to evaluate, which is (5x+2y):(3x-y) . This can be written as a fraction: 5x+2y/3x-y Substitute x=2k and y=3k into the numerator: 5x+2y = 5(2k) + 2(3k) = 10k + 6k = 16k Substitute x=2k and y=3k into the denominator: 3x-y = 3(2k) - (3k) = 6k - 3k = 3k Now, form the ratio using the simplified numerator and denominator: $$ 5x+2y3x-y

If $x:y = 2:3$, then $(5x+2y):(3x-y) = $

The correct answer is Option b: $16:3$. To determine the ratio $(5x+2y):(3x-y)$, we first use the given information about the ratio of $x$ to $y$. Given that $x:y = 2:3$. This can be expressed as a fraction: $$ \frac{x}{y} = \frac{2}{3} $$ From this relationship, we can introduce a common non-zero constant, say $k$, such that: $$ x = 2k $$ $$ y = 3k $$ Since $x:y = 2:3$, neither $x$ nor $y$ can be zero, which implies that $k \neq 0$. Now, we substitute these expressions for $x$ and $y$ into the ratio we need to evaluate, which is $(5x+2y):(3x-y)$. This can be written as a fraction: $$ \frac{5x+2y}{3x-y} $$ Substitute $x=2k$ and $y=3k$ into the numerator: $$ 5x+2y = 5(2k) + 2(3k) $$ $$ = 10k + 6k $$ $$ = 16k $$ Substitute $x=2k$ and $y=3k$ into the denominator: $$ 3x-y = 3(2k) - (3k) $$ $$ = 6k - 3k $$ $$ = 3k $$ Now, form the ratio using the simplified numerator and denominator: $$ \frac{5x+2y}{3x-y

Ratio, Proportion, Indices, LogarithmMCQMTP June 22Question 836 of 305

All Questions

If $\displaystyle x:y = 2:3$ , then $\displaystyle (5x+2y):(3x-y) =$

Options

\displaystyle 19:3

\displaystyle 16:3

\displaystyle 7:2

\displaystyle 7:3

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Correct Answer

✅ Option b — $\displaystyle 16:3$

All Options:

A $\displaystyle 19:3$
B $\displaystyle 16:3$
C $\displaystyle 7:2$
D $\displaystyle 7:3$

Detailed Solution & Explanation

To determine the ratio

\displaystyle (5x+2y):(3x-y)

, we first use the given information about the ratio of

\displaystyle x

\displaystyle y

. Given that

\displaystyle x:y = 2:3

. This can be expressed as a fraction:

\frac{x}{y} = \frac{2}{3}

From this relationship, we can introduce a common non-zero constant, say

\displaystyle k

, such that:

x = 2k

y = 3k

Since

\displaystyle x:y = 2:3

, neither

\displaystyle x

nor

\displaystyle y

can be zero, which implies that

\displaystyle k \neq 0

. Now, we substitute these expressions for

\displaystyle x

and

\displaystyle y

into the ratio we need to evaluate, which is

\displaystyle (5x+2y):(3x-y)

. This can be written as a fraction:

\frac{5x+2y}{3x-y}

Substitute

\displaystyle x=2k

and

\displaystyle y=3k

into the numerator:

5x+2y = 5(2k) + 2(3k)

= 10k + 6k

= 16k

Substitute

\displaystyle x=2k

and

\displaystyle y=3k

into the denominator:

3x-y = 3(2k) - (3k)

= 6k - 3k

= 3k

Now, form the ratio using the simplified numerator and denominator: $$ \frac{5x+2y}{3x-y

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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If x:y=2:3\displaystyle x:y = 2:3x:y=2:3, then (5x+2y):(3x−y)=\displaystyle (5x+2y):(3x-y) =(5x+2y):(3x−y)=