Question

8. Two numbers are such that the ratio between them is 3:5. If each is increased
by 10, the ratio between new numbers so formed is 5:7. Find the smallest
original number
A. 15
B. 11
C. 7
D. 5​

Answer 1

Answer:

Given :-

• Two numbers are such that the ratio between them is 3 : 5.
• If each is increased by 10, the ratio between new numbers so formed is 5 : 7.

To Find :-

• What is the smallest original number.

Solution :-

Let,

$\mapsto \bf{First\: Number =\: 3x}$

$\mapsto \bf{Second\: Number =\: 5x}$

➦ 10 is increased in both the numbers :

$\leadsto \sf First\: Number =\: 3x + 10$

$\leadsto \sf Second\: Number =\: 5x + 10$

According to the question,

$\implies \bf (3x + 10) : (5x + 10) =\: 5 : 7$

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

By doing cross multiplication we get,

$\implies \sf 5(5x + 10) =\: 7(3x + 10)$

$\implies \sf 25x + 50 =\: 21x + 70$

$\implies \sf 25x - 21x =\: 70 - 50$

$\implies \sf 4x =\: 20$

$\implies \sf x =\: \dfrac{20}{4}$

$\implies \sf\bold{\purple{x =\: 5}}$

Hence, the required numbers are :

❒ First Number :

$\longrightarrow \sf First\: Number =\: 3x$

$\longrightarrow \sf First\: Number =\: 3 \times 5$

$\longrightarrow \sf\bold{\red{First\: Number =\: 15}}$

❒ Second Number :

$\longrightarrow \sf Second\: Number =\: 5x$

$\longrightarrow \sf Second\: Number =\: 5 \times 5$

$\longrightarrow \sf\bold{\red{Second\: Number =\: 25}}$

${\small{\bold{\underline{\therefore\: The\: smallest\: original\: number\: is\: 15\: .}}}}$

Hence, the correct options is option no (A) 15.

Answer 2

Step-by-step explanation:

$\underline{\purple{\ddot{\Mathsdude}}}$

To prove :-

• The smallest original number.

Explanation :-

• Let ,
• First number should be 3 x
• Second number should be 5x

♧♧Here 10 is increased in both of the numbers.

• Then numbers be

1. First number should be =3x+1
2. Second number should be =5x+10

♧♧According to the given question :-

• (3x+10) : (5x+10)=5:7

• 3x+10/5x+10=5/7

♧♧Now by doing cross multiplication we get

• 5(5x+10) = 7 (3x+10)

• 25x+50 =21x +70

• 25x -21 x = 70-50

• 4x = 20

• x =20/4

• x = 5

♧♧Hence here required numbers are:-

• First number =3x

=3×5

• =15

• Second number =5x

=5×5

=25.

♧♧Therefore, the smallest original number is 15.

♧♧Hope it helps u mate .

♧♧Thank you .