Question

Two numbers are such that the ratio between them is 3:5. If each is increased by 10, the ratio between the new numbers so formed is 5:7. find the original numbers.​

Answer 1

Let the numbers be 3x and 5x,

3x+10=5x and 5x+10=7x

2x=10 2x=10

x=5 x=5

The numbers are 3x = 15 and 5x = 25.

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Answer 2

Given :-

• Two numbers are such that the ratio between them is 3:5.

• If each is increased by 10,the ratio between the new number so formed is 5:7.

To find :-

• The original numbers = ?

Solution :-

Let the first number be 3x

and second number be 5x

⪼ when 10 is increased in both numbers then, the new number formed 5:7

• 3x + 10 : 5x + 10 = 5 : 7

According to the question,

$\rm\longrightarrow\dfrac{3x+10}{5x+10}=\dfrac{5}{7}$

By cross multiplication,

$\rm\longrightarrow\:5(5x+10)=7(3x+10)$

$\rm\longrightarrow\:25x+50=21x+70$

$\rm\longrightarrow\:25x-21x=70-50$

$\rm\longrightarrow\:4x=20$

$\rm\longrightarrow\:x=\cancel\dfrac{20}{4}$

$\rm\longrightarrow\:x=5$

Now,

First number = 3x = 3 × 5 = 15

Second number = 5x = 5 × 5 = 25

Hence, the original numbers will be 15 and 25.