The ratio compounded of 4:5 and sub-duplicate of A:9 is 8:15 . Then value of " A " is

Option b: 3. Solution: Let the first ratio be R1 = 4:5 . Let the second ratio be the sub-duplicate of A:9 . The sub-duplicate ratio of x:y is given by sqrt(x):sqrt(y) . Therefore, the second ratio R2 is sqrt(A):sqrt(9) . Since sqrt(9)=3 , the second ratio R2 is sqrt(A):3 . The compounded ratio of two ratios a:b and c:d is (a × c) : (b × d) . We need to find the ratio compounded of R1 = 4:5 and R2 = sqrt(A):3 . The compounded ratio is (4 × sqrt(A)) : (5 × 3) . This simplifies to 4sqrt(A) : 15 . According

The ratio compounded of $4:5$ and sub-duplicate of $A:9$ is $8:15$. Then value of "$A$" is

The correct answer is Option b: $3$. Let the first ratio be $R_1 = 4:5$. Let the second ratio be the sub-duplicate of $A:9$. The sub-duplicate ratio of $x:y$ is given by $\sqrt{x}:\sqrt{y}$. Therefore, the second ratio $R_2$ is $\sqrt{A}:\sqrt{9}$. Since $\sqrt{9}=3$, the second ratio $R_2$ is $\sqrt{A}:3$. The compounded ratio of two ratios $a:b$ and $c:d$ is $(a \times c) : (b \times d)$. We need to find the ratio compounded of $R_1 = 4:5$ and $R_2 = \sqrt{A}:3$. The compounded ratio is $(4 \times \sqrt{A}) : (5 \times 3)$. This simplifies to $4\sqrt{A} : 15$. According

Ratio, Proportion, Indices, LogarithmMCQMTP March 22Question 834 of 305

All Questions

The ratio compounded of $\displaystyle 4:5$ and sub-duplicate of $\displaystyle A:9$ is $\displaystyle 8:15$ . Then value of " $\displaystyle A$ " is

Options

\displaystyle 2

\displaystyle 3

\displaystyle 4

\displaystyle 5

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — $\displaystyle 3$

All Options:

A $\displaystyle 2$
B $\displaystyle 3$
C $\displaystyle 4$
D $\displaystyle 5$

Detailed Solution & Explanation

Let the first ratio be

\displaystyle R_1 = 4:5

.
Let the second ratio be the sub-duplicate of

\displaystyle A:9

.
The sub-duplicate ratio of

\displaystyle x:y

is given by

\displaystyle \sqrt{x}:\sqrt{y}

.
Therefore, the second ratio

\displaystyle R_2

\displaystyle \sqrt{A}:\sqrt{9}

.
Since

\displaystyle \sqrt{9}=3

, the second ratio

\displaystyle R_2

\displaystyle \sqrt{A}:3

.
The compounded ratio of two ratios

\displaystyle a:b

and

\displaystyle c:d

\displaystyle (a \times c) : (b \times d)

.
We need to find the ratio compounded of

\displaystyle R_1 = 4:5

and

\displaystyle R_2 = \sqrt{A}:3

.
The compounded ratio is

\displaystyle (4 \times \sqrt{A}) : (5 \times 3)

.
This simplifies to

\displaystyle 4\sqrt{A} : 15

.
According

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.

Ready to Master Ratio, Proportion, Indices, Logarithm?

Practice all 305 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free

The ratio compounded of 4:5\displaystyle 4:54:5 and sub-duplicate of A:9\displaystyle A:9A:9 is 8:15\displaystyle 8:158:15. Then value of "A\displaystyle AA" is