Two numbers are such that if 7 is added to the smaller number then their sum becomes double of the larger number and if 4 is added to the larger number then their sum becomes three times the smaller number. Find both the numbers.
Let the larger number be x and smaller be y
When 7 is added to the smaller number their sum becomes double of the larger number
y + 7 = 2x
⇒ y = 2x - 7 …equation (i)
When 4 is added to the larger number their sum becomes three times of the smaller number
x + 4 = 3y
⇒ x = 3y - 4 ……equation(ii)
Putting the value of y in equation (ii) we get
x = 3(2x - 7) - 4
⇒ x = 6x - 21 - 4
5x = 25
⇒ x = 5
y = 2x – 7
Now putting the value of x in this equation
Y = 2 x 5 – 7
⇒ y = 3
Answer: The numbers are 5 and 3
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