Ratio, Proportion, Indices, LogarithmsPYQ May 25Question 4001 of 220
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The sum of three numbers is 98. If the ratio of the first to second number is 2:3 and that of the second to third is 5:8, then the second number is

Options

A20
B30
C48
D58
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Correct Answer

✅ Option b — 30

All Options:

  • A20
  • B30
  • C48
  • D58

Detailed Solution & Explanation

Let the three numbers be represented as x\displaystyle x, y\displaystyle y, and z\displaystyle z.
According to the problem, the sum of the three numbers is:
x+y+z=98x + y + z = 98
The ratio of the first to the second number is:
x:y=2:3x : y = 2 : 3
The ratio of the second to the third number is:
y:z=5:8y : z = 5 : 8
To combine these two ratios into a single ratio x:y:z\displaystyle x : y : z, we make the term for y\displaystyle y equal in both ratios by finding the Least Common Multiple (LCM) of 3\displaystyle 3 and 5\displaystyle 5, which is 15\displaystyle 15.
Multiplying the first ratio by 5\displaystyle 5:
x:y=(2×5):(3×5)=10:15x : y = (2 \times 5) : (3 \times 5) = 10 : 15
Multiplying the second ratio by 3\displaystyle 3:
y:z=(5×3):(8×3)=15:24y : z = (5 \times 3) : (8 \times 3) = 15 : 24
Therefore, the combined ratio is:
x:y:z=10:15:24x : y : z = 10 : 15 : 24
Let x=10k\displaystyle x = 10k, y=15k\displaystyle y = 15k, and z=24k\displaystyle z = 24k for some constant k\displaystyle k.
Substitute these values into the sum equation:
10k+15k+24k=9810k + 15k + 24k = 98
49k=9849k = 98
k=9849=2k = \frac{98}{49} = 2
Now, we can find the second number y\displaystyle y:
y=15k=15×2=30y = 15k = 15 \times 2 = 30
Hence, **Option B** is the correct answer.

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