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

Answer :-

Let the numbers be 3x and 5x

Each is increased by 10 :-

New numbers = 3x + 10 , 5x + 10

According to the question :-

→ 3x + 10 / 5x + 10 = 5 / 7

→ 7 ( 3x + 10 ) = 5 ( 5x + 10 )

→ 21x + 70 = 25x + 50

→ 25x - 21x = 70 - 50

→ 4x = 20

→ x = 20/4

→ x = 5

Numbers = 3x = 3 × 5 = 15

5x = 5 × 5 = 25

Required Numbers = 15 and 25

Verification :-

Numbers = 15 and 25

Ratio - 15 : 25 = 3 : 5

10 is added :-

New Numbers = 25 and 35

Ratio - 25 : 35 = 5 : 7

Hence verified.

Answer 2

Answer:

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 :-

• The required numbers are 15 and 25.

Given :-

• Ratio between two numbers = 3 : 5.
• Each number is increased by 10. And so,
• New ratio formed between numbers = 5 : 7.

To find :-

• We have to find the numbers.

Step-by-step explanation :-

• As we are given that the ratio between the two numbers is 3 : 5.
• So, let the two numbers be 3x and 5x.
• We are also given that, each number is increased by 10.
• So our new numbers are 3x + 10 and 5x + 10.
• So firstly, by using a required equation we will find out the value of x.

Required equation is as follows :-

${\underline{\boxed{\sf {\dfrac{x}{y}\ =\ \dfrac{5}{7}}}}}$

Here,

• x = 3x + 10.
• y = 5x + 10.

By applying the values, we get :-

$\sf \mapsto {\dfrac{x}{y}\ =\ \dfrac{5}{7}}$

$\sf \mapsto {\dfrac{3x\ +\ 10}{5x\ +\ 10}\ =\ \dfrac{5}{7}}$

$\sf \mapsto {7(3x\ +\ 10)\ =\ 5(5x\ +\ 10)}$

$\sf \mapsto {21x\ +\ 70\ =\ 25x\ +\ 50}$

$\sf \mapsto {25x\ -\ 21x\ =\ 70\ -\ 50}$

$\sf \mapsto {4x\ =\ 20}$

$\sf \mapsto {x\ =\ \cancel \dfrac{20}{4}}$

${\therefore{\underline{\boxed{\tt {x\ =\ 5.}}}}}$

• Now we have the value of x. So, by multiplying the assumed numbers with the value of x, we will find out the numbers.

$\sf \mapsto {3x\ =\ 3 \times 5}$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\underline{\boxed{\tt {15.}}}}$

$\sf \mapsto {5x\ =\ 5 \times 5}$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\underline{\boxed{\tt {25.}}}}$

${\therefore{\underline{\sf{\pmb{Hence,\ the\ required\ numbers\ are\ {\red {15}\ and\ {\red {25}.}}}}}}}$