If the ratio of two numbers is 7:11 . If 7 is added to each number then the new ratio will be 2:3 then the numbers are.

Option a: 49,77. Solution: Let the two numbers be 7x and 11x . According to the problem, adding 7 to both numbers yields a ratio of 2 : 3 : 7x + 7/11x + 7 = 2/3 Cross-multiplying to solve for x : 3(7x + 7) = 2(11x + 7) 21x + 21 = 22x + 14 22x - 21x = 21 - 14 x = 7 The original numbers are: - First number: 7x = 7(7) = 49 - Second number: 11x = 11(7) = 77 Thus, the numbers are 49 and 77 .

If the ratio of two numbers is $7:11$. If $7$ is added to each number then the new ratio will be $2:3$ then the numbers are.

The correct answer is Option a: $49,77$. Let the two numbers be $7x$ and $11x$. According to the problem, adding $7$ to both numbers yields a ratio of $2 : 3$: $$\frac{7x + 7}{11x + 7} = \frac{2}{3}$$ Cross-multiplying to solve for $x$: $$3(7x + 7) = 2(11x + 7)$$ $$21x + 21 = 22x + 14$$ $$22x - 21x = 21 - 14 \implies x = 7$$ The original numbers are: - First number: $7x = 7(7) = 49$ - Second number: $11x = 11(7) = 77$ Thus, the numbers are $49$ and $77$.

Ratio, Proportion, Indices, LogarithmMCQPYQ June 19Question 790 of 305

All Questions

If the ratio of two numbers is $\displaystyle 7:11$ . If $\displaystyle 7$ is added to each number then the new ratio will be $\displaystyle 2:3$ then the numbers are.

Options

\displaystyle 49,77

\displaystyle 42,45

\displaystyle 43,42

\displaystyle 39,40

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

Correct Answer

✅ Option a — $\displaystyle 49,77$

All Options:

A $\displaystyle 49,77$
B $\displaystyle 42,45$
C $\displaystyle 43,42$
D $\displaystyle 39,40$

Detailed Solution & Explanation

Let the two numbers be

\displaystyle 7x

and

\displaystyle 11x

.
According to the problem, adding

\displaystyle 7

to both numbers yields a ratio of

\displaystyle 2 : 3

\frac{7x + 7}{11x + 7} = \frac{2}{3}

Cross-multiplying to solve for

\displaystyle x

3(7x + 7) = 2(11x + 7)

21x + 21 = 22x + 14

22x - 21x = 21 - 14 \implies x = 7

The original numbers are:
- First number:

\displaystyle 7x = 7(7) = 49

- Second number:

\displaystyle 11x = 11(7) = 77

Thus, the numbers are

\displaystyle 49

and

\displaystyle 77

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

If the ratio of two numbers is 7:11\displaystyle 7:117:11. If 7\displaystyle 77 is added to each number then the new ratio will be 2:3\displaystyle 2:32:3 then the numbers are.