Question

1. Two numbers are in the ratio 2:3. The larger number is 30 more than half of the smaller
number. Find the numbers.​

Answer 1

Answer :

The required numbers are 30 and 45.

Step-by-step explanation :

Given :

• Two numbers are in the ratio 2:3
• The larger number is 30 more than half of the smaller  number.

To find :

the numbers

Solution :

Since the two numbers are in the ratio 2 : 3,

let the numbers be

• 2x
• 3x

The larger number is 3x and

the smaller number is 2x

The relation between larger number and smaller number is given as

the larger number is 30 more than half the smaller number.

   $\sf 3x=\bigg(\dfrac{2x}{2}\bigg) +30$

  3x = x + 30

  3x - x = 30

   2x = 30

    x = 30/2

    x = 15

Substitute the value of x,

 3x = 3(15) = 45

 2x = 2(15) = 30

The numbers are 30 and 45.

Verification :

Condition - 1 : Two numbers are in the ratio 2:3

 $\dfrac{30}{45}=\dfrac{2}{3} \\\\ \dfrac{3 \times 10}{3 \times 15}=\dfrac{2}{3} \\\\ \dfrac{10}{15}=\dfrac{2}{3} \\\\ \dfrac{5 \times 2}{5 \times 3}=\dfrac{2}{3} \\\\ \dfrac{2}{3}=\dfrac{2}{3}$

LHS = RHS

Condition - 2 : the larger number is 30 more than half the smaller number

  45 = 30/2 + 30

  45 = 15 + 30

  45 = 45

  LHS = RHS

Hence verified!