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SSC CGL 2022 PYQ — Question 59

SSC CGL - 21 April 2022 - Shift 3 • Quantitative Aptitude • Q59

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LCM and HCF of two numbers are 90 and 15, respectively. If the sum of the two numbers is 75, then find the greater number.

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 45

Let the two nos. be a and b,

So, a + b = 75

⇒ (a + b)2 = 5625

⇒ a2 + b2 + 2ab = 5625

⇒ a2 + b2 + 2 × 90 × 15 = 5625

⇒ a2 + b2 = 2925

Now,

⇒ (a - b)2 = a2 + b2 - 2ab

⇒ 2925 - 2700 = (a - b)2

⇒ 225 = (a - b)2

⇒ 15 =  (a - b)

Now, from equation 1 and 2,

a = 45 and b = 30

The greater number is 45.