Ratio, Proportion, Indices, LogarithmMCQMTP Dec 22 Series IIQuestion 840 of 302
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What must be added to each term of the ratio $49:68$. So that it becomes $3:4$?

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c — 8\displaystyle 8

All Options:

  • A3\displaystyle 3
  • B5\displaystyle 5
  • C8\displaystyle 8
  • D9\displaystyle 9

Detailed Solution & Explanation

Let the given ratio be $49:68$. This can be expressed as a fraction $4968\displaystyle \frac{49}{68}$.
Let x\displaystyle x be the quantity that must be added to each term of the ratio.
When x\displaystyle x is added to each term, the new terms become (49+x)\displaystyle (49+x) and (68+x)\displaystyle (68+x).
The new ratio is then (49+x):(68+x)\displaystyle (49+x):(68+x), which can be written as the fraction 49+x68+x\displaystyle 49+x68+x\displaystyle \frac{49+x}{68+x}.
According to the problem statement, this new ratio must be equal to $3:4$.
Therefore, we can set up the following equation: 49+x68+x=3449+x68+x=34\displaystyle \frac{49+x}{68+x} = \frac{3}{4} To solve for x\displaystyle x, we will cross-multiply the terms of the equation:
4(49+x)=3(68+x)4(49+x) = 3(68+x) Now, distribute the numbers on both sides of the equation:
(4×49)+(4×x)=(3×68)+(3×x)(4 ×\displaystyle \times 49) + (4 ×\displaystyle \times x) = (3 ×\displaystyle \times 68) + (3 ×\displaystyle \times x) Perform the multiplications:
196+4x=204+3x196 + 4x = 204 + 3x To isolate x\displaystyle x, we need to gather all terms containing x\displaystyle x on one side and constant terms on the other side. Subtract $3x$ from both sides of the equation:
196+4x−3x=204+3x−3x196 + 4x - 3x = 204 + 3x - 3x 196+x=204196 + x = 204 Next, subtract $196$ from both sides of the equation to find the value of $x$:
196+x−196=204−196196 + x - 196 = 204 - 196 x=8x = 8 To verify our answer, substitute x=8\displaystyle x=8 back into the original ratio terms:
New first term: $49+8 = 57$
New second term: $68+8 = 76$
The new ratio is $57:76$.
To check if this ratio simplifies to $3:4\displaystyle , we can divide both terms by their greatest common divisor. We observe that $57 = 3 ×\displaystyle \times 19 and $76 = 4 ×\displaystyle \times 19$.
So, the ratio $57:76$ can be written as $(3 ×\displaystyle \times 19):(4 ×\displaystyle \times 19)$, which simplifies to $3:4$.
This confirms that our calculated value of x=8\displaystyle x=8 is correct.
Comparing this result with the given options, x=8\displaystyle x=8 corresponds to Option C. Therefore, the correct choice is **Option C**.

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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