Question

A natural number when subtracted from 28, becomes equal to 160 times its reciprocal. Find the number.

Answer 1

Given:-

• A natural number when subtracted from 28, becomes equal to 160 times its reciprocal.

To find:-

• The number.

Solution:-

Let,

• the natural no. be x.

According to the question,

→ 28 - x = 160 × 1/x

→ 28 - x = 160/x

→ x(28 - x) = 160/x

→ 28x - x² = 160

→ x² - 28x + 160 = 0

→ x² - 20x - 8x + 160 = 0

→ x(x - 20) - 8(x - 20) = 0

→ (x - 20) (x - 8) = 0

→ (x - 20) = 0, (x - 8) = 0

→ x = 20, x = 8

Hence,

• the numbers are 20 and 8.

Answer 2

28 - x = 160/x

Multiply by x to get x2 - 28x + 160 = 0

(x - 20)(x - 8) = 0

x = 20 or 8

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