Question

the two numbers are in the ratio Set 5:7
adding 1 to the first and 3 to the
second their ratio becomes 6/9.
Find the numbers.​

Answer 1

AnswEr:-

→ Numbers = 15 & 21

$\rule{200}{1}$

Given:-

• Two numbers are in ratio of 5 : 7

• Adding 1 to the first & 3 to the second,ratio becomes : 6 : 9

To find:-

• What are the numbers?

Solution:-

Case 1:-

As the numbers are in the ratio of 5 : 7

So,let the numbers as 5n & 7n.

Case 2:-

Adding 1 to 5n & 3 to 7n ratio = 6 : 9

According to question:-

⇒ (5n + 1) : (7n + 3) = 6 : 9

⇒ (5n + 1)/(7n + 3) = 6/9

After cross multiplication —

⇒ 9(5n + 1) = 6(7n + 3)

⇒ 45n + 9 = 42n + 18

⇒ 45n - 42n = 18 - 9

⇒ 3n = 9

⇒ n = 9/3

⇒ n = 3

★ Two numbers:-

⇒ 1st number = 5n

⇒ 1st number = 5(3)

⇒ 1st number = 15

$\rule{180}{2}$

⇒ 2nd number = 7n

⇒ 2nd number = 7(3)

⇒ 2nd number = 21

Therefore,

Two numbers are 21 & 15 .

Answer 2

Answer:

• Let the Numbers be 5x and 7x.
• After Adding 1 to first number and 3 to second number.
• New Ratio will be = 6 : 9

$\underline{\bigstar\:\:\textsf{According to the Question :}}$

$\dashrightarrow\tt\:\:\dfrac{5x+1}{7x+3}=\dfrac{6}{9}\\\\{\scriptsize\qquad\bf{\dag}\:\:\textsf{By Cross Multiplication.}}\\\\\dashrightarrow\tt\:\:9(5x + 1) = 6(7x + 3)\\\\\\\dashrightarrow\tt\:\:45x + 9 = 42x + 18\\\\\\\dashrightarrow\tt\:\:45x - 42x = 18 - 9\\\\\\\dashrightarrow\tt\:\:3x = 9\\\\\\\dashrightarrow\tt\:\:x = \dfrac{9}{3}\\\\\\\dashrightarrow\tt\:\:x = 3$

$\rule{150}{1}$

$\underline{\bigstar\:\:\textsf{Numbers are :}}$

$\bullet\:\:\textsf{First Number = 5x = 5(3) = \textbf{15}}\\\bullet\:\:\textsf{Second Number = 7x = 7(3) = \textbf{21}}$