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The sum of two number, when multiplied with each of the number separately, then the results of these multiplication are 2418 and 3666, respectively. Find the difference between the numbers. ?
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- 16
- 21
- 19
- 23
Correct Option: A
Let the number be x and y.
Now, according to the question,
x(x + y) = 2418 .....(i)
and y(x + y) = 3666 .....(ii)
On adding Eqs. (i) and (ii), we get
x2 + xy + yx + y2 = 6084
⇒ x2 + 2xy + y2 = 6084
⇒ (x + y)2 = 6084
∴ x + y = √6084 = 78
On subtracting Eq. (ii) from Eq. (i), we get
x2 + xy - yx - y2 = -1248
⇒ x2 - y2 = -1248
⇒ (x + y) (x - y) = -1248
⇒ 78(x - y) = -1248
⇒ x - y = - 1248 / 78 = -16
⇒ (y - x) = 16
