Question

Ratio of two numbers is 3:8. On adding 5 to both numbers, the ratio becomes 2:5. Which is the smaller number out of the two? ​

Answer 1

✬ Smaller Number = 45 ✬

Step-by-step explanation:

Given:

• Ratio of two numbers is 3:8.
• After adding 5 to both numbers ratio becomes 2:5.

To Find:

• Which is the smaller number ?

Solution: Let one number be x and other number be y. Therefore,

➟ First number/Second number = 3/8

➟ x/y = 3/8

➟ 8x = 3y

➟ x = 3y/8ㅤㅤㅤㅤㅤ(i)

[ Now adding 5 to both numbers ]

• One number = x + 5

• Other number = y + 5

• New ratio = 2:5

$\implies{\rm }$ (x + 5)/(y + 5) = 2/5

$\implies{\rm }$ 5(x + 5) = 2(y + 5)

$\implies{\rm }$ 5x + 25 = 2y + 10

$\implies{\rm }$ 5(3y/8) – 2y = 10 – 25

$\implies{\rm }$ 15y – 16y/8 = – 15

$\implies{\rm }$ – y = – 15 × 8

$\implies{\rm }$ y = 120

Now put the value of y in equation (i).

➮ x = 3 × 120/8

➮ x = 360/8 = 45

Hence, the smaller number out of the two is 45.

Answer 2

Answer:

The smaller number is 45.

Step-by-step explanation:

Given :-

Ratio of two numbers is 3 : 8. On adding 5 to both numbers, the ratio becomes 2 : 5.

To find :-

Smaller number out of the two numbers.

Solution :-

Let the first number be 3x and the second number be 8x.

Accordingly, 5 is added to both numbers and ratio becomes 2 : 5.

(3x + 5)/(8x + 5) = 2/5

Cross multiply,

5(3x + 5) = 2(8x + 5)

15x + 25 = 16x + 10

15x - 16x = 10 - 25

-x = -15

x = 15

Required numbers,

3x = 45

8x = 120

∴ The smaller number is 45.