The LCM of two numbers is 240 times their HCF, and the sum of their LCM and HCF is 17593. One of these two numbers, when divided by 125, the quotient is 8 and the remainder is 95. The other number is:  

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AAI Junior Assistant (Fire Service) Official Paper (Held On: 15 Nov 2022 Shift 1)
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  1. 1241
  2. 1095
  3. 1314
  4. 1168

Answer (Detailed Solution Below)

Option 4 : 1168
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Detailed Solution

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Given:

LCM = 240 × HCF

LCM + HCF = 17593

One number when divided by 125 gives quotient = 8 and remainder = 95

Formula Used:

Product of two numbers = HCF × LCM

Calculation:

LCM + HCF = 17593 and LCM = 240 × HCF:

⇒ 240 × HCF + HCF = 17593

⇒ 241 × HCF = 17593

⇒ HCF = 17593 ÷ 241 = 73

LCM = 240 × 73

⇒ LCM = 17520

First number = 125 × 8 + 95

⇒ First number = 1000 + 95 = 1095

Product of two numbers = HCF × LCM

⇒ 1095 × Second number = 73 × 17520

⇒ Second number = (73 × 17520) /1095 = 1168

∴ The correct answer is 1168.

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