Question

The ratio of two numbers is 5 : 7. If 40 is added in each number, then the ratio becomes25 : 31, Find the numbers.
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Answer 1

Solution :

Two numbers are 60 and 84

Step by step explanation:

Let the two numbers be 5x and 7x

Ratio$\sf=\dfrac{5x}{7x}=\dfrac{5}{7}$

According to the question :

If 40 is added in each number then the ratio becomes 25:31 , then

$\sf\dfrac{5x+40}{7x+40}=\dfrac{25}{31}$

$\sf\implies(5x+40)31=25(7x+40)$

$\sf\implies\:5x\:\times31+40\times\:31=25\times7x+25\times40$

$\sf\implies\:155x+1240=175x+1000$

$\sf\implies\:1240-1000=175x-155x$

$\sf\implies\:20x=240$

$\sf\implies\:x=\dfrac{240}{20}$

$\sf\implies\:x=12$

Thus , Two numbers

• $\sf\:5x=12\times5=60$
• other one $\sf\:7x=12\times7=84$

Answer 2

Answer:

✯ Given :-

• The ratio of two numbers is 5:7. If 40 is added in each number, then the ratio becomes 25:31 .

✯ To Find :-

• What is the numbers.

✯ Solution :-

» The ratio of two numbers is 5:7.

» Let, the rational between two number be x

» Thus, the two number are 5x and 7x

» If 40 is added in each number, then the ratio becomes 25:31 .

» By adding 40 the first number becomes 5x + 40 and the second number be 7x + 40

➣ According to the question,

⇒ $\dfrac{5x + 40}{7x + 40}$ = $\dfrac{25}{31}$

By doing cross multiplication we get,

⇒ 25(7x + 40) = 31(5x+ 40)

⇒ 175x + 1000 = 155x + 1240

⇒ 175x - 155x = 1240 - 1000

⇒ 20x = 240

⇒ x = $\sf\dfrac{\cancel{240}}{\cancel{20}}$

➠ x = 12

Hence, the rational number is 12.

Thus, the two number are :-

❒ First number = 5x = 5 × 12 = 60

❒ Second number = 7x = 7 × 12 = 84

$\therefore$ The two numbers are 60 and 84 .

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