Question

Two numbers are in the ratio 3:4, if 6 be added to each term of the ratio, than the new ratio will be 4:5, then the numbers are
a. 14,20
b. 17, 19
c. 18, 24
(give the full solution)​

Answer 1

Answer :

Given :

• Two no(s) are in ratio = 3:4

• Final ratio when 6 is added to both no(s) = 4:5

To Find :

• Numbers

Solution :

➪ Let the number be x , then two no(s) become 3x and 4x .

When 6 is added to both side ,

$\implies \sf 3x\:+\:6$

$\implies \sf 4x\:+\:6$

• According to the question :

$\implies \sf \dfrac{3x\:+\:6}{4x\:+\:6}\:=\: \dfrac{4}{5}$

• On Solving :

$\implies \sf 5(3x\:+\:6)\:=\:4(4x\:+\:6)$

$\implies \sf 15x\:+\:30\:=\:16x\:+\:24$

$\implies \sf 16x\:-\:15x\:=\:30\:-\:24$

$\implies \large{\boxed{\sf{\red{x\:=\: 6}}}}$

• Numbers are : 18 and 24

➪ First number = 3(6) = 18

➪ Second number = 4(6) = 24

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Answer 2

AnswEr :-

• 18 and 24.

Given :-

• Two numbers are in the ratio 3 : 4 and 6is added to each term then new ratio will be 4 : 5.

To Find :-

• These numbers

SoluTion :-

Put x in the ratio.

Numbers are

• 3x
• 4x

When 6 is added to both sides :-

• 3x + 6
• 4x + 6

• The new ratio will be 4 : 5.

According to question :-

→ $\frac{3x + 6}{4x + 6} = \frac{4}{5}$

→ $5(3x + 6) = 4(4x + 6)$

→ $15x + 30 = 16x + 24$

→ $30 - 24 = 16x - 15x$

→ $x = 6$

Put the value of x in the ratio :-

• 1st no. = 3x = 3 × 6 = 18
• 2nd no. = 4x = 4 × 6 = 24

Hence, the numbers are 18 and 24 respectively.

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