Ratio, Proportion, Indices, LogarithmMCQMTP Dec 22 Series IIQuestion 840 of 305
All Questions

What must be added to each term of the ratio 49:68\displaystyle 49:68. So that it becomes 3:4\displaystyle 3:4?

Options

A3\displaystyle 3
B5\displaystyle 5
C8\displaystyle 8
D9\displaystyle 9
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — 8\displaystyle 8

All Options:

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

Ad

Detailed Solution & Explanation

Let the given ratio be 49:68\displaystyle 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 \frac{49+x}{68+x}.
According to the problem statement, this new ratio must be equal to 3:4\displaystyle 3:4.
Therefore, we can set up the following equation: 49+x68+x=34\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 \times 49) + (4 \times x) = (3 \times 68) + (3 \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\displaystyle 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\displaystyle 196 from both sides of the equation to find the value of x\displaystyle 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\displaystyle 49+8 = 57
New second term: 68+8=76\displaystyle 68+8 = 76
The new ratio is 57:76\displaystyle 57:76.
To check if this ratio simplifies to 3:4\displaystyle 3:4, we can divide both terms by their greatest common divisor. We observe that 57=3×19\displaystyle 57 = 3 \times 19 and 76=4×19\displaystyle 76 = 4 \times 19.
So, the ratio 57:76\displaystyle 57:76 can be written as (3×19):(4×19)\displaystyle (3 \times 19):(4 \times 19), which simplifies to 3:4\displaystyle 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.

More Questions from Ratio, Proportion, Indices, Logarithm

3x−2:5x+6\displaystyle 3x-2:5x+6 the duplicate ratio of 2:3\displaystyle 2:3 then find the value x\displaystyle x.

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

If x:y=z:7=4:11\displaystyle x:y=z:7=4:11 then x+y+zz\displaystyle \frac{x+y+z}{z} is

The ratio of two numbers are 3:4\displaystyle 3:4. The difference of their squares is 28\displaystyle 28 greater is:

The price of scooter and moped are in the ratio 7:9\displaystyle 7:9. The price of moped is ₹1,600\displaystyle ₹1,600 more than that of scooter. Then the price of moped is:

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

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