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The product of two successive integral multiples of 5 is 300. Determine the multiples.

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11,15

13,15

22,12

15,20

answer is D.

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Detailed Solution

Given,
Product of two successive multiples of 5 is 300.
Assume the multiples as 5 x and

5 (x + 1)

where x is an integer.

⇒ (5 x) × 5 (x + 1) = 300 ⇒ 25 x (x + 1) = 300 ⇒ x (x + 1) = 12 ⇒ x 2 + x − 12 = 0

Solve the quadratic equation using the formula to find the values of x.

x = − 1 ± (1) 2 − 4 × 1 × (− 12) 2 × 1 ⇒ x = − 1 ± 1 + (4 × 12) 2 ⇒ x = − 1 ± 1 + 48 2

⇒ x = − 1 ± 49 2 ⇒ x = − 1 ± 7 2

That is, x can be

− 1 + 7 2 or − 1 − 7 2

x = − 1 + 7 2 ⇒ x = 62 ⇒ x = 3

The numbers will be 5 x and

5 (x + 1)

.
That is, the numbers can be 15 and 20

x = − 1 − 7 2 ⇒ x = − 8 2 ⇒ x = − 4

The numbers will be 5 x and

5 (x + 1)

.
That is, the numbers can be -20 and -15.
Thus, the numbers can be 15 and 20 or -20 and -15 and the correct option is 4.

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