Question

The smaller of numbers is two thirds of the greater.If their sum is 120,find the numbers.

Answer 1

Answer = 72 and 48 Solution- Say the two numbers are x and y. x is smaller and y bigger x=2y/3 ..equation 1 and, x+y=120 ..equation 2 Putting equation 1 in equation 2 2y/3+y=120 (2+3)y/3=120 5y=120×3=360 y=360/5=72 So x =120-72 or 72/3×2= 48 So the two numbers are 72 and 48.

Answer 2

Given:

Sum of the two is 120 and the smallest one is $\frac {2}{3}$ of the largest one.

To find:

The numbers X and Y

Answer:

Assume smaller numbers are X and Y

X is smaller and Y is bigger

$X = \frac {2}{3} \times Y ------ (1)$

The sum is $X + Y = 120 --- (2)$

Substitute the X value in equation 2

$\frac {2}{3} \times Y + Y = 120$

$\frac {2Y+3Y}{3} = 120$

$2Y+3Y = 360$

$5Y = 360$

$Y = 72$

Put Y = 72 in equation 1

$X= \frac {2}{3} \times 72 = 48$

$X = 48 \quad and \quad Y = 72$