Question

The ratio of the nurabers is 5:7. If 40 is added in each number, then
the ratio becomes 25:31. Find the smaller number.​

Answer 1

Answer:

The smaller number is $60$

Step-by-step explanation:

Let the numbers be 5x and 7x.

new numbers: 5x+40, 7x+40

$\frac{5x+40}{7x+40} = \frac{25}{31}\\{31(5x+40)} = 25(7x+40)\\155x + 1240 = 175x + 1000\\240 = 20x\\x = 12$

The numbers are $5x = 5*12 = 60\\7x = 7*12 = 84$

Answer 2

The ratio of two numbers is 5:7

Let the rational between two numbers be x.

Thus the two numbers are 5x and 7x

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

On adding 40 the first number become 5x + 40 and the second number 7x + 40

Their ratio 5x + 40 / 7x + 40 become 25 : 31

5x + 40 / 7x + 40 = 25 / 31

Cross multiplication

25 (7x + 40) = 31 (5x + 40)

175x + 1000 = 155x + 1240

175x - 155x = 1240 - 1000

20x = 240

x = 240/20

x = 12

The rational is 12. Thus the two numbers are :-

First number 5x = 5 × 12 = 60

Second number 7x = 7 × 12 = 84

Answer :- The two numbers are 60 and 84.

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