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The product of two numbers is 24 times the difference of these two numbers. If the sum of these numbers is 14, the larger number is
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- 9
- 8
- 7
- 10
Correct Option: B
Let the first number be x.
∴ Second number = 14–x
∴ x (14 – x ) = 24 (x – 14 + x)
⇒ x (14 – x ) = 24 (2x – 14)
⇒ 14x – x2 = 48x – 336
⇒ x2 + 34x – 336 = 0
⇒ x2 + 42x – 8x – 336 = 0
⇒ x (x + 42) – 8 (x + 42) = 0
⇒ (x + 42) (x – 8) = 0
∴ x = 8 as x ≠ – 42
∴ Second number = 14 – 8 = 6
∴ Larger number = 8
Note : : It is preferable to solve it
by oral calculation with the help
of given alternatives.
