Question

15. Find two numbers whose sum is 100 and whose ratio is 9:16.​

Answer 1

Answer: 36, 64

Step-by-step explanation:

The ratio of two number =9:16

Let the number be 9x and 16x

The sum of the two numbers =100

∴(9x+16x)=100

⟹9x+16x=100⟹25x=100

⟹x= 100/25  

​  

=4

Required numbers are  9×4=36 and 16×4=64.

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Answer 2

Given:

Two numbers

• In ratio 9 : 16
• Sum = 100

What To Find:

We have to find the two numbers.

How To Find:

To find the two numbers we will

• Take x as common multiple in the ratio 9 : 16 = 9x : 16x
• Form the equation like this 9x + 16x = 100

Solution:

9x + 16x = 100

Add the terms in LHS,

⇒ 25x = 100

Take 25 to RHS,

⇒ x = $\dfrac{100}{25}$

Divide 100 by 25,

⇒ x = 4

Now substitute the values,

• 9x = 9 × 4 = 36
• 16x = 16 × 4 = 64

∴ Hence, the two numbers are 36 and 64 respectively.

Verification:

9x + 16x = 100

Substitute the values,

⇒ 9(4) + 16(x) = 100

Multiple the brackets,

⇒ 36 + 64 = 100

Add 36 and 64,

⇒ 100 = 100

∴ LHS = RHS

∴ Hence verified.