Question

The ratio of monthly salary of Nithin and Gokul is 7:8, their respective
monthly expenditure are in the ratio 2:3. Nithin saves one third of his
income.What is the ratio of the savings of Nithin to that of Gokul?​

Answer 1

$★ {\pmb{\underline{\sf{Required \ Solution ... }}}}$

As We know that the ratio of monthly salary of Nithin and Gokul is 7:8 Respectively.

Let the Salary of Nithin and Gokul be 7x and 8x Respectively.

»Their Monthly Expenditure be 2y and 3y Respectively.

★Nithin's Savings be like:

• 7x - 2y

★ Gokul's Savings be like:

• 8x - 3y

~As We also know that Nithin saves one third of his income as.

$\colon\implies{\tt{ 7x - 2y = \dfrac{1}{3} (7x) }} \\ \\ \colon\implies{\tt{ 7x - 2y = \dfrac{7x}{3} }} \\ \\ \colon\implies{\tt{ 21x - 6y = 7x }} \\ \\ \colon\implies{\tt{ 6y = 21x - 7x }} \\ \\ \colon\implies{\tt{ y = \dfrac{14x}{6} = \dfrac{7x}{3} \ \ \ \ \ \cdots(1) }}$

Now, Finally We can compare the Savings of Nithin and Gokul and got the desired Ratio of savings of Nithin to that of Gokul as.

$\colon\implies{\tt{ \dfrac{7x-2y}{8x-3y } }} \\ \\ \colon\implies{\tt{ \dfrac{7x-2 \times \dfrac{7x}{3} }{ 8x - \cancel{3} \times \dfrac{7x}{ \cancel{3} } } }} \\ \\ \colon\implies{\tt{ \dfrac{7x - \dfrac{14x}{3} }{ 8x - 7x } }} \\ \\ \colon\implies{\tt{ \dfrac{ \dfrac{21x-14x}{3} }{x} }} \\ \\ \colon\implies{\tt{ \dfrac{7 \cancel{x} }{3 \cancel{x} } = \dfrac{7}{3} }} \\ \\ \colon\implies{\tt{ 7 \colon 3 }}$

Hence,

The Ratio of the savings of the Nithin to that of the savings of the Gokul will be 7:3 as Well.