Question

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 1

(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.