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SSC Selection Post 2022 PYQ — Question 62

SSC Selection Post - Matriculation Level 2022 - 2 Feb 2022 - Shift 3 • Quantitative Aptitude • Q62

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If (3x - 10)% of 150 exceeds x% of 300 by 15, then by what percent is (2x + 5)% of 220 more than (x + 10)% of 250?

 

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 32%

(3x−10)100×150−x100×300=15\frac{(3x - 10)}{100} \times 150 - \frac{x}{100} \times 300 = 15

⇒150(3x−10)−300x100=15⇒450x−1500−300x100=15⇒150x−1500100=15⇒150x−1500=1500⇒x=3000150=20(2x+5)% of 220=(2×20+5)%×220=45%×220=0.45×220=99(x+10)% of 250=(20+10)%×250=30%×250=0.3×250=75\Rightarrow \frac{150(3x - 10) - 300x}{100} = 15 \\ \Rightarrow \frac{450x - 1500 - 300x}{100} = 15 \\ \Rightarrow \frac{150x - 1500}{100} = 15 \\[5pt] \Rightarrow 150x - 1500 = 1500 \Rightarrow x = \frac{3000}{150} = 20 \\[10pt] (2x + 5)\% \text{ of } 220 = (2 \times 20 + 5)\% \times 220 = 45\% \times 220 = 0.45 \times 220 = 99 \\[5pt] (x + 10)\% \text{ of } 250 = (20 + 10)\% \times 250 = 30\% \times 250 = 0.3 \times 250 = 75 \\[5pt]

 Difference = 99 - 75 = 24

Percentage more than 75 :

2475×100=32%\quad \frac{24}{75} \times 100 = 32\%