Question

The ratio of two numbers are 3:5 if 10 is add in each number the new ratio become 5:7 then find out the smaller number?​

Answer 1

Given :

• The ratio of two numbers are 3:5 .
• If 10 is added to each number the new ratio become 5:7 .

To Find :

• Smaller number .

Solution :

$\longmapsto\tt{Let\:one\:first\:be=3x}$

$\longmapsto\tt{Let\:second\:number\:be=5x}$

Now ,

• If 10 is added to each number the new ratio become 5:7 .

$\longmapsto\tt{First\:number=3x+10}$

$\longmapsto\tt{Second\:number=5x+10}$

A.T.Q :

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

$\longmapsto\tt{7(3x+10)=5(5x+10)}$

$\longmapsto\tt{21x+70=25x+50}$

$\longmapsto\tt{21x-25x=50-70}$

$\longmapsto\tt{-4x=-20}$

$\longmapsto\tt{x=\cancel\dfrac{-20}{-4}}$

$\purple\longmapsto\:\large\underline{\boxed{\bf\blue{x}\pink{=}\red{5}}}$

Therefore :

$\longmapsto\tt{First\:Number=3(5)}$

$\longmapsto\tt\bf{15}$

$\longmapsto\tt{Second\:Number=5(5)}$

$\longmapsto\tt\bf{25}$

So , First number(15) is smaller than second .

Answer 2

Answer:

• Smaller number = 15

Explanation:

Given information,

The ratio of two numbers is 3:5 if 10 is add in each number the new ratio become 5:7 then find out the smaller number?

• Ratio of two numbers = 3:5
• Ratio of two number after adding 10 to both = 5:7
• Smaller number = ?

Let,

• Two numbers = 3y and 5y.

According to the Question,

• Ratio of two number after adding 10 to both = 5:7

Therefore,

➻ (3y + 10)/(5y + 10) = 5/7

By doing cross multiplication,

➻ 7(3y + 10) = 5(5y + 10)

➻ 21y + 70 = 25y + 50

➻ 21y - 25y = 50 - 70

➻ -4y = -20

➻ 4y = 20

➻ y = 20/4

➻ y = 5

So,

◐ First number = 3y

◐ First number = 3 × 5

◐ First number = 15

Also,

◐ Second number = 5y

◐ Second number = 5 × 5

◐ Second number = 25

ㅤㅤFirst number < Second number

ㅤㅤㅤㅤㅤㅤㅤ15 < 25

• Henceforth, the smaller number is 15 respectively.

Verification:

• Ratio of two number after adding 10 to both = 5:7

Therefore,

➻ (3y + 10)/(5y + 10) = 5/7

Putting value of y,

➻ (3 × 5 + 10)/(5 × 5 + 10) = 5/7

➻ (15 + 10)/(25 + 10) = 5/7

➻ 25/35 = 5/7

➻ 5/7 = 5/7

➻ LHS = RHS

Hence, Verified ✔

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