If three times the larger of the two numbers is divided by the smaller

1.	If three times the larger of the two numbers is divided by the smaller one, we get 4 as quotient and 3 as the remainder. Also if seven times the smaller number is divided by the larger one, we get 5 as quotient and 1 as remainder. Find the sum of the numbers. (a) 34 (b) 43 (c) 47 (d) 74
Answer» (b) 43 Let the larger number be x and the smaller one be y. We know that, Dividend = (Divisor × Quotient) + Remainder By the first condition, 3x = 4y + 3 \(\Rightarrow\) 3x – 4y = 3 ........(i) By the second condition, 7y = 5x + 1 \(\Rightarrow\) 5x – 7y = –1 .........(ii) Now we can easily get x and y.

If three times the larger of the two numbers is divided by the smaller one, we get 4 as quotient and 3 as the remainder. Also if seven times the smaller number is divided by the larger one, we get 5 as quotient and 1 as remainder. Find the sum of the numbers. (a) 34 (b) 43 (c) 47 (d) 74

Answer»

(b) 43

Let the larger number be x and the smaller one be y.

We know that,

Dividend = (Divisor × Quotient) + Remainder

By the first condition,

3x = 4y + 3 \(\Rightarrow\) 3x – 4y = 3 ........(i)

By the second condition,

7y = 5x + 1 \(\Rightarrow\) 5x – 7y = –1 .........(ii)

Now we can easily get x and y.