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The sum of two numbers is 75 and their difference is 25. The product of the two numbers is :
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- 1350
- 1250
- 125
- 1000
Correct Option: B
Let the numbers be p and q .
According to the question,
p + q = 75
p – q = 25
∴ (p + q )2 − (p − q )2 = 4pq
⇒ 752 – 252 = 4pq
⇒ 4pq = (75 + 25) (75 – 25)
[∵ a2 − b2 = (a + b )(a − b)]
⇒ 4pq = 100 × 50
| ⇒ pq = | = 1250 | |
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