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The difference between two numbers is 9 and the difference between their squares is 207. The numbers are :
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- 17 and 8
- 16 and 7
- 15 and 6
- 23 and 14
Correct Option: B
Let the numbers be a and b where a > b.
According to the question,
a – b = 9 .... (i)
and a2 – b2 = 207
⇒ (a + b) (a – b) = 207
⇒ 9 (a + b) = 207
| ⇒ a + b = | = 23 .... (ii) | |
| 9 |
On adding equations (i) and (ii),
a + b + a – b = 23 + 9
⇒ 2a = 32 ⇒ a = 16
∴ a – b = 9
⇒ 16 – b = 9
⇒ b = 16 – 9 = 7
