Q5 of 80 Page 56

Find three consecutive numbers such that if they are divided by 10, 17, and 26 respectively, the sum of their quotients will be 10.

(Hint: Let the consecutive numbers = x, x + 1, x + 2, then)

Let the three consecutive numbers be x, x + 1 and x + 2.

The quotient when


x is divided by 10 =


x + 1 is divided by 17 =


x + 2 is divided by 26 =


The sum of the quotients = 10.


According to the given condition,



⇒ (LCM of 10, 17 and 26 is 2210)




⇒ (Multiply by 2210 on both sides)


436x + 300 = 22100


⇒ 436x = 22100 – 300 (Transposing 300 to RHS)


436x = 21800


⇒ x = (Transposing 436 to RHS)


x = 50


The three consecutive numbers are


x = 50


x + 1 = 50 + 1 = 51


x + 2 = 50 + 2 = 52


∴ The three consecutive numbers are 50, 51 and 52.


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