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Question : The difference between the cubes of two given natural numbers is 6272, while the positive difference between the two given numbers is 8. What is the product of the two given numbers?

Option 1: 160

Option 2: 240

Option 3: 200

Option 4: 320


Team Careers360 22nd Jan, 2024
Answer (1)
Team Careers360 23rd Jan, 2024

Correct Answer: 240


Solution : Let the numbers be x and y.
So, x 3 – y 3 = 6272 and (x – y) = 8
Cubing both sides of the given expression, (x – y) = 8,
⇒ (x – y) 3 = 8 3
⇒ x 3 – y 3 – 3xy(x – y) = 512
⇒ 6272 – 3xy × 8 = 512
⇒ 24xy = 5760
⇒ xy = 240
Hence, the correct answer is 240.

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