Question

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

Answer 1

let the no.s br 5x and 7x respectively
ATQ
5x+40÷7x+40=25÷31
31×5x+40 = 7x+40 × 25
65x+1240 = 175x +800
65x - 175x = 800- 1240
-110x= -440
110x = 440
x= 440 ÷ 110
x= 4
if x= 4 then first no. = 5×4 = 20
= 7 ×4 =28

Answer 2

Question :

The ratio of two numbers is 5 : 7 . if 40 is added in each number, then the ratio become 25 : 31. Find the numbers.

Given :

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

Required to Find :

The numbers.

Solution :

Let the first number be 5x and second number be 7x.

From the given condition,

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

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

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

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

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

$\sf \implies \: x = 12$

Therefore, First number = 5 × 12 = 60 and second number = 7 × 12 = 84

Hence, given numbers are 60 and 84

More

• Ratio of number a and b is written as a : b or \dfrac{a}{b}. a is called as the predecessor ( first term ) and b is called as the succesor ( Second term )
• In the ratio of two numbers, if the second term is 100 then it is known as a percentage .
• The quantities taken in the ratio must be expressed in the same unit.