If A:B=3:7 , then 3a+2b:4a+5b=?

Option a: 23:47. Solution: Given the ratio a : b = 3 : 7 , we can write a = 3k and b = 7k . Substituting these values into the ratio 3a + 2b : 4a + 5b : 3a + 2b/4a + 5b = 3(3k) + 2(7k)/4(3k) + 5(7k) = 9k + 14k/12k + 35k = 23k/47k = 23/47 Thus, the ratio is 23 : 47 .

If $A:B=3:7$, then $3a+2b:4a+5b=?$

The correct answer is Option a: $23:47$. Given the ratio $a : b = 3 : 7$, we can write $a = 3k$ and $b = 7k$. Substituting these values into the ratio $3a + 2b : 4a + 5b$: $$\frac{3a + 2b}{4a + 5b} = \frac{3(3k) + 2(7k)}{4(3k) + 5(7k)}$$ $$= \frac{9k + 14k}{12k + 35k} = \frac{23k}{47k} = \frac{23}{47}$$ Thus, the ratio is $23 : 47$.

Ratio, Proportion, Indices, LogarithmMCQPYQ Nov 20Question 793 of 305

All Questions

If $\displaystyle A:B=3:7$ , then $\displaystyle 3a+2b:4a+5b=?$

Options

\displaystyle 23:47

\displaystyle 27:43

\displaystyle 24:51

\displaystyle 29:53

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Correct Answer

✅ Option a — $\displaystyle 23:47$

All Options:

A $\displaystyle 23:47$
B $\displaystyle 27:43$
C $\displaystyle 24:51$
D $\displaystyle 29:53$

Detailed Solution & Explanation

Given the ratio

\displaystyle a : b = 3 : 7

, we can write

\displaystyle a = 3k

and

\displaystyle b = 7k

.
Substituting these values into the ratio

\displaystyle 3a + 2b : 4a + 5b

\frac{3a + 2b}{4a + 5b} = \frac{3(3k) + 2(7k)}{4(3k) + 5(7k)}

= \frac{9k + 14k}{12k + 35k} = \frac{23k}{47k} = \frac{23}{47}

Thus, the ratio is

\displaystyle 23 : 47

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 A:B=3:7\displaystyle A:B=3:7A:B=3:7, then 3a+2b:4a+5b=?\displaystyle 3a+2b:4a+5b=?3a+2b:4a+5b=?