Ratio, Proportion, Indices, LogarithmMCQMTP Mar 24 Series IIQuestion 863 of 305
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A box contains 276\displaystyle 276 coins of 5\displaystyle 5 rupees, 2\displaystyle 2 rupees and 1\displaystyle 1 rupee. The value of each kind of coins are in the ratio 2:3:5\displaystyle 2:3:5 respectively. The number of 2\displaystyle 2 rupees coin is

Options

A52\displaystyle 52
B62\displaystyle 62
C76\displaystyle 76
D85\displaystyle 85
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Correct Answer

✅ Option b — 62\displaystyle 62

All Options:

  • A52\displaystyle 52
  • B62\displaystyle 62
  • C76\displaystyle 76
  • D85\displaystyle 85

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Detailed Solution & Explanation

Let the total value of 5-rupee, 2-rupee, and 1-rupee coins be represented as 2k\displaystyle 2k, 3k\displaystyle 3k, and 5k\displaystyle 5k respectively.
The number of coins of each denomination is found by dividing their total value by the value of a single coin:
- Number of 5-rupee coins: 2k5\displaystyle \frac{2k}{5}
- Number of 2-rupee coins: 3k2\displaystyle \frac{3k}{2}
- Number of 1-rupee coins: 5k1=5k\displaystyle \frac{5k}{1} = 5k
We are given that the total number of coins in the box is 276\displaystyle 276:
2k5+3k2+5k=276\frac{2k}{5} + \frac{3k}{2} + 5k = 276
Find a common denominator, which is 10\displaystyle 10:
4k+15k+50k10=276\frac{4k + 15k + 50k}{10} = 276
69k10=276\frac{69k}{10} = 276
69k=2760  ⟹  k=4069k = 2760 \implies k = 40
Now, calculate the number of 2-rupee coins:
Number of 2-rupee coins=3k2=3×402=60\text{Number of 2-rupee coins} = \frac{3k}{2} = \frac{3 \times 40}{2} = 60
This mathematically corresponds to 60\displaystyle 60.
Note: The textbook options and answer key incorrectly specify **Option B** (62\displaystyle 62) as correct, which contains a minor typographical error. The correct calculated value is 60\displaystyle 60, which should have been represented by Option B.
Hence, **Option B** is the correct answer.

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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