Question

12. A number is divided into two parts such that one part is 10 more than the other. If the two parts ar
in the ratio 5:3, find the number and the two parts.

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Answer 1

GIVEN:

• One part of the number is 10 more than the other.
• The two parts are in the ratio 5:3.

TO FIND:

• What are the two parts ?

SOLUTION:

Let one number be 'x' and another number be 'y'

CONDITION:- 1]

One part of the number is 10 more than the other.

$\bf{\hookrightarrow x = y + 10...1) }$

CONDITION:- 2]

The two parts are in the ratio 5:3.

$\rm{\hookrightarrow \dfrac{x}{y} = \dfrac{5}{3}}$

$\bf{\hookrightarrow 3x = 5y....2) }$

Put the value of 'x' from equation 1) in equation 2)

$\rm{\hookrightarrow 3(y +10) = 5y }$

$\rm{\hookrightarrow 3y + 30 = 5y}$

$\rm{\hookrightarrow 30 = 5y - 3y }$

$\rm{\hookrightarrow 30 = 2y }$

$\rm{\hookrightarrow \cancel\dfrac{30}{2} = y}$

$\bf{\hookrightarrow 15 = y }$

Put the value of 'y' in equation 1)

$\rm{\hookrightarrow x = 15 + 10 }$

$\bf{\hookrightarrow x = 25 }$

❝ Hence, the two divided parts are 25 and 15 ❞

______________________

Answer 2

Question= A number is divided into two parts such that one part is 10 more than the other. If the two parts are in the ratio 5:3, find the number and the two parts.

To find:

Number and two parts.

Solution⬇️

One part x then other part is x+10

(x+10):x::5:3

Or, 3x+30=5x

Or, x=15Numbers are 15,25

I hope it helps all.

If you don't understand answer then see that above pic⤴️