Question

Ratio between two numbers is 4: 7. If each is increased by 20, then the ratio becomes 7:9,find the number​

Answer 1

Answer:

Given :-

• The ratio between the two numbers is 4 : 7.
• Each is increased by 20, then the ratio becomes 7 : 9.

To Find :-

• What is the number.

Solution :-

Let,

➲ First Number = 4a

➲ Second Number = 7a

According to the question,

$\bigstar$ Each is increased by 20, then the ratio becomes 7 : 9.

$\implies \sf \bigg\{\dfrac{First\: Number + 20}{Second\: Number + 20}\bigg\} =\: \bigg\{\dfrac{7}{9}\bigg\}$

$\implies \sf \dfrac{4a + 20}{7a + 20} =\: \dfrac{7}{9}$

By doing cross multiplication we get,

$\implies \sf 7(7a + 20) =\: 9(4a + 20)$

$\implies \sf 49a + 140 =\: 36a + 180$

$\implies \sf 49a - 36a =\: 180 - 140$

$\implies \sf 13a =\: 40$

$\implies \sf\bold{\purple{a =\: \dfrac{40}{13}}}$

Hence, the required numbers are :

❒ First Number :

$\longrightarrow \sf First\: Number =\: 4a$

$\longrightarrow \sf First\: Number =\: 4\bigg(\dfrac{40}{13}\bigg)$

$\longrightarrow \sf First\: Number =\: 4 \times \dfrac{40}{13}$

$\longrightarrow \sf\bold{\red{First\: Number =\: \dfrac{160}{13}}}$

❒ Second Number :

$\longrightarrow \sf Second\: Number =\: 7a$

$\longrightarrow \sf Second\: Number =\: 7\bigg(\dfrac{40}{13}\bigg)$

$\longrightarrow \sf Second\: Number =\: 7 \times \dfrac{40}{13}$

$\longrightarrow \sf\bold{\red{Second\: Number =\: \dfrac{280}{13}}}$

${\small{\bold{\underline{\therefore\: The\: numbers\: are\: \dfrac{160}{13}\: and\: \dfrac{280}{13}\: .}}}}$

Answer 2

Answer:

$\green{ \boxed{ \leadsto\bf \: {1}^{{st} } \: \: number \: = \frac{160}{13} }} \\ \\ \orange{ \boxed{ \leadsto \: \bf {2}^{{nd}} \: \: number = \frac{280}{13} }}$

Step-by-step explanation:

Given,

→ The ratio between the two numbers is = 4:7

Again,

→ If each is increased by 20, then the ratio becomes =7:9

To Find :

★ Those two number.

Solution :

Let assume that, common ratio is = x

So,

→ 1st Number = 4x

→ 2nd Number = 7x

Now each is increased by 20 and after that the ratio becomes = 7 : 9

So,

$\bf \: \frac{4x + 20}{7x + 20} = \frac{7}{9} \\ \bf \implies \: 9 \times (4x + 20) = 7 \times (7x + 20) \\ \bf \implies \: 36x + 180 = 49x + 140 \\ \bf \implies \: 49x - 36x = 180 - 140 \\ \bf \implies \: 13x = 40 \\ \bf \implies \: x = \frac{40}{13}$

Now,

$\green{ \leadsto\bf \: {1}^{{st} } \: \: number \: = 4x = 4 \times \frac{40}{13} = \frac{160}{13} } \\ \\ \orange{ \leadsto \: \bf {2}^{{nd}} \: \: number = 7x = 7 \times \frac{40}{13} = \frac{280}{13} }$