Question

9. The difference of two whole numbers is
25. The ratio of two numbers is 28:23.
What are the numbers?​

Answer 1

Step-by-step explanation:

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Answer 2

ANSWER :

• ❖ If the difference of two whole numbers is 25 and the ratio of two numbers is 28 : 23; then the whole numbers are 140 and 115.

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SOLUTION :

❒ Given :-

• Difference between two whole numbers = 25

• The ratio of two numbers = 28 : 23

❒ To Find :-

• The numbers = ?

❒ Calculation Method 1 :-

Suppose,

• ★ One of the whole number = x

According to first condition,

• ★ Another whole number = x - 25

According to second condition,

• $\bigstar \: \: \: \sf{\dfrac{x}{x - 25} = \dfrac{28}{23}}$

➨ 28 (x - 25) = 23x

➨ 28 x - 700 = 23x

➨ 28x - 23x = 700

➨ 5x = 700

➨ x = $\sf{\frac{700}{5}}$

∴ x = 140

• ➜ The one of the whole number is = x = 140

• ➜ Another whole number is = x - 25 = 140 - 25 = 115

Hence,

• ✎ The two whole numbers are 140 and 115.

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❒ Calculation Method 2 :-

We have,

• Ratio of the two whole numbers = 28 : 23

Suppose,

• The constant is = x

Then,

• ★ One of the whole number = 28x

• ★ Another whole number = 23x

Again,

• Difference between the whole numbers = 25

According to question,

• ★ 28x - 23x = 25

➨ 5x = 25

➨ x = $\sf{\frac{25}{5}}$

➨ x = 5

Substituting the value of constant, we get,

• ➜ One of the whole number = 28x = 28 × 5 = 140

• ➜ Another whole number = 23x = 23 × 5 = 115

Hence,

• ✎ The whole numbers are 140 and 115.