Question

two numbers are such that the ratio is 3 is to 5 if each is increased by 10 the ratio between the New numbers so formed is 5 is to 7.find the original numbers ​

Answer 1

Answer:

x = 5

3x = 15

5x = 25

Step-by-step explanation:

The ratio between two numbers is : 3:5

Let 3 be 3x and 5 be 5x.

Then,

3x+10:5x+10 = 5:7

The same written in fractional form=

3x/5x + 10/10 = 5/7

7(3x+10) = 5(5x+10)

21x + 70 = 25x + 50

21x - 25 = 50 - 70

4x = 20

x = 20/4

x = 5

3x = 15

5x = 25

Answer 2

Question : -

Two numbers are in the ratio of 3 : 5 . If each number is increased by 10 the ratio of the new numbers which are formed will be in the ratio of 5 : 7 .

Find the original number ?

Given : -

Two numbers are in the ratio of 3 : 5 .

If each number is increased by 10 the ratio of the new numbers which are formed will be in the ratio of 5 : 7 .

Required to find : -

• Original number ?

Solution : -

Two numbers are in the ratio of 3 : 5 .

If each number is increased by 10 the ratio of the new numbers which are formed will be in the ratio of 5 : 7 .

We need to find the original number .

So,

Given ratio = 3 : 5

Now,

Let the 1st number be 3x

2nd number be 5x

Here,

x is a variable which represents an unknown value .

If we are able to calculate the value of x then we can find the original number .

However,

a : b = a/b ( a : b can also be written as a/b )

This implies ;

Ratio of the two numbers = 3x/5x

Now,

According to the 2nd statement .

If each number is increased by 10 the ratio of the new numbers which are formed will be in the ratio of 5 : 7 .

So,

Let the 1st number be 3x + 10

2nd number be 5x + 10

According to the condition ;

These two numbers when increased by 10 will be equal to ratio 5 : 7

This implies ;

$\tt{\bf{\pink{ \dfrac{ 3x + 10}{ 5x + 10 } = \dfrac{ 5}{ 7 }}}}$

By cross multiplication we get ;

7 ( 3x + 10 ) = 5 ( 5x + 10 )

21x + 70 = 25x + 50

21x - 25x = 50 - 70

- 4x = - 20

Taking - ( minus ) common on both sides

- ( 4x ) = - ( 20 )

- ( minus ) get's cancelled on both sides

4x = 20

x = 20/4

x = 5

Hence,

• Value of x = 5

Now,

By substituting these value x in place of x in the assumed values

This implies ;

1st number = 3x

=> 3 ( 5 )

=> 15

2nd number = 5x

=> 5 ( 5 )

=> 25

Therefore,

The original number are 15 & 25 .

Verification : -

Let's verify whether our calculations are correct or wrong .

For that , let's consider the 2nd statement .

According to which ;

The two numbers when increased by 10 will be equal to ratio 5 : 7

So,

The two numbers will thus become as ;

15 + 10 = 25

25 + 10 = 35

This implies ;

25 : 35 = 5 : 7

By reducing using the 5 table we get ;

5 : 7 = 5 : 7

LHS = RHS

Hence Verified !