Question

Two numbers are in the ratio 4. 5. If 5 is added to each number, the ratio becomes 13:16. Find the numbers. ​

Answer 1

Answer:

Given :-

• Two numbers are in the ratio is 4 : 5.
• 5 is added to each number, the ratio becomes 13 : 16.

To Find :-

• What is the numbers.

Solution :-

Let,

➲ First Number = 4x

➲ Second Number = 5x

✭ 5 is added to each number :

➟ First Number = (4x + 5)

➟ Second Number = (5x + 5)

According to the question,

$\implies \sf \bf \bigg\{\dfrac{4x + 5}{5x + 5}\bigg\} =\: \bigg\{\dfrac{13}{16}\bigg\}$

$\implies \sf \dfrac{4x + 5}{5x + 5} =\: \dfrac{13}{16}$

By doing cross multiplication we get,

$\implies \sf 13(5x + 5) =\: 16(4x + 5)$

$\implies \sf 65x + 65 =\: 64x + 80$

$\implies \sf 65x - 64x =\: 80 - 65$

$\implies \sf\bold{\purple{x =\: 15}}$

Hence, the required numbers are :

✰ First Number :

➵ First Number = 4x

➵ First Number = 4 × 15

➢ First Number = 60

✰ Second Number :

➵ Second Number = 5x

➵ Second Number = 5 × 15

➣ Second Number = 75

$\therefore$ The numbers is 60 and 75 .