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Mathematics

Six more than one-fourth of a number is two fifth of the number. Find the number.

Linear Eqns One Variable

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Answer

Let the number be x.

So,

⇒6+14x=25x⇒6=25x−14x⇒ 6 + \dfrac{1}{4}x = \dfrac{2}{5}x\\[1em] ⇒ 6 = \dfrac{2}{5}x - \dfrac{1}{4}x

Since L.C.M. of denominators 5 and 4 = 20, multiply each term with 20 to get:

⇒6×20=2×205x−1×204x⇒ 6 \times 20 = \dfrac{2 \times 20}{5}x - \dfrac{1 \times 20}{4}x

⇒ 120 = 2 ×\times 4x - 1 ×\times 5x

⇒ 120 = 8x - 5x

⇒ 120 = 3x

⇒ x = 1203\dfrac{120}{3}

⇒ x = 40

Hence, the number is 40.

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