Two numbers are such that if 7 is added to the smaller number, then th

1.	Two numbers are such that if 7 is added to the smaller number, then the sum is twice the greater and if 4 is added to the greater number, then the sum is thrice the smaller number. Find the two numbers.
Answer» Let two numbers are x and y, where x > y y + 7 = 2x or 2x – y = 7 …(i) also x + 4 = 3y or x – 3y = – 4 …(ii) Multiplying equation (ii) by 2 and then subtracting from (i), we get 5y = 15 ⇒ y = 3 Now substituting the value of y in (i), we get 2x – 3 = 7 or 2x = 10 or x = 5 Hence, required numbers are 5 and 3.

Two numbers are such that if 7 is added to the smaller number, then the sum is twice the greater and if 4 is added to the greater number, then the sum is thrice the smaller number. Find the two numbers.

Answer»

Let two numbers are x and y, where x > y

y + 7 = 2x

or 2x – y = 7 …(i)

also x + 4 = 3y

or x – 3y = – 4 …(ii)

Multiplying equation (ii) by 2 and then subtracting from (i), we get

5y = 15 ⇒ y = 3

Now substituting the value of y in (i), we get

2x – 3 = 7

or 2x = 10

or x = 5

Hence, required numbers are 5 and 3.