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A number when divided by 3, leaves a remainder of 1 with a quotient of Q1. When the same number is divided by 5, it leaves a remainder of 3 with a quotient of Q2. If 5Q1 + 5Q2 = 110, find the ratio Q1/Q2.

A number when divided by 3, leaves a remainder of 1 with a quotient of Q1. When the same number is divided by 5, it leaves a remainder of 3 with a quotient of Q2. If 5Q1 + 5Q2 = 110, find the ratio Q1/Q2. Correct Answer 7/4

Let the number be ‘x’

⇒ x = 3Q1 + 1

Also, x = 5Q2 + 3

Hence, we have,

⇒ 3Q1 + 1 = 5Q2 + 3

⇒ 3Q1 - 5Q2 = 2      ----(1)

Given, 5Q1 + 5Q2 = 110      ----(2)

Adding (1) and (2),

⇒ 3Q1 - 5Q2 + 5Q1 + 5Q2 = 110 + 2

⇒ 8Q1 = 112

⇒ Q1 = 112/8 = 14

Substituting in (2),

⇒ Q2 = (110 - 70)/5 = 8

∴ Q1/Q2 = 14/8 = 7/4

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