Three consecutive whole numbers are such that if they be divided by 5, 3 and 4 respectively, the sum of the quotients is 40. Find the numbers.
Linear Eqns One Variable
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Question

Three consecutive whole numbers are such that if they be divided by 5, 3 and 4 respectively, the sum of the quotients is 40. Find the numbers.

KnowledgeBoat · Accepted Answer

Let the three consecutive whole numbers be (x \- 1), x, (x \+ 1). According to the question, the sum of the quotients is 40. Since L.C.M. of denominators 5, 3 and 4 = 60, multiply each term with 60 to get: ⇒ (x - 1) 12 + x 20 + (x + 1) 15 = 2400\\[1em] ⇒ (12x - 12) \+ 20x \+ (15x \+ 15) = 2400 ⇒ 12x - 12 + 20x + 15x + 15 = 40 ⇒ 47x + 3 = 2400 ⇒ 47x = 2400 - 3 ⇒ 47x = 2397 ⇒ x = ⇒ x = 51 Other number = (x - 1), (x + 1) = (51 - 1), (51 + 1) = 50, 52 Hence, the numbers are 50, 51 and 52.

Mathematics

Three consecutive whole numbers are such that if they be divided by 5, 3 and 4 respectively, the sum of the quotients is 40. Find the numbers.

Linear Eqns One Variable

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