Q16 of 102 Page 49

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


More from this chapter

All 102 →
15

Find the solution of the system of equations

 15

Find the solution of the system of equations

 16

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.

 17

The numerator of any fraction is 4 less than the denominator. If 2 is subtracted From the numerator and 1 is added to denominator then denominator becomes 8 times the numerator. Find the fraction.