Ratio, Proportion, Indices, LogarithmsPYQ Jan 26Question 4249 of 220
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In India, an examination is conducted in two sessions. In the first session the ratio of boys to girls among 455 students is 8: 5. If 50 new girls are admitted in the second session, how many new boys must be admitted so that the ratio of girls to boys becomes 3: 4?

Options

A20
B30
C40
D50
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Correct Answer

✅ Option a — 20

All Options:

  • A20
  • B30
  • C40
  • D50

Detailed Solution & Explanation

Given:
- Total number of students in the first session = 455\displaystyle 455
- Ratio of boys to girls in the first session = 8:5\displaystyle 8 : 5

Let us calculate the number of boys and girls in the first session:
Sum of ratio terms=8+5=13\text{Sum of ratio terms} = 8 + 5 = 13
Number of boys=813×455=8×35=280\text{Number of boys} = \frac{8}{13} \times 455 = 8 \times 35 = 280
Number of girls=513×455=5×35=175\text{Number of girls} = \frac{5}{13} \times 455 = 5 \times 35 = 175

In the second session:
- 50\displaystyle 50 new girls are admitted. So, new number of girls = 175+50=225\displaystyle 175 + 50 = 225.
- Let x\displaystyle x be the number of new boys admitted. So, new number of boys = 280+x\displaystyle 280 + x.
- The new ratio of **girls to boys** is given as 3:4\displaystyle 3 : 4.

Set up the proportion:
New number of girlsNew number of boys=34\frac{\text{New number of girls}}{\text{New number of boys}} = \frac{3}{4}225280+x=34\frac{225}{280 + x} = \frac{3}{4}
Cross-multiply to solve for x\displaystyle x:
3(280+x)=4(225)3(280 + x) = 4(225)
840+3x=900840 + 3x = 900
3x=900−8403x = 900 - 840
3x=603x = 60
x=20x = 20
Thus, 20\displaystyle 20 new boys must be admitted.

Hence, **Option A** is the correct answer.

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