When a number is successively divided by 3, 4 and 7, the remainder obtained is 2, 3 and 5, respectively. What will be the remainder when 42 divides the same number?

29

Given,

Divisors = 3, 4 and 7

Remainders = 2, 3 and 5

We know,

(Divisor × Quotient) + Remainder = Dividend

Let a be the number

Let b and c be the quotients

⇒ c = 7 × 1 + 5 = 12

⇒ b = 4 × c + 3

⇒ b = 4 × 12 + 3 = 51

⇒ a = 3 × b + 2

⇒ a = 3 × 51  + 2 = 155

Now, \(\frac{155}{42}\) = 29 Remainder