# The monthly pocket money of Ravi and Sanjeev are in the ratio 5:7. Their expenditures are in ratio 3:5. If each saves Rs.80 every month, find their monthly pocket money.

Answer

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Hint: In this question we have been given the ratios of pocket money and expenditures, we also know the savings so, we need to find their monthly pocket money. To do so we will assume their pocket money to be 5x and 7x and expenditures to be 3y and 5y then solve. This would help us simplify the thing and reach the solution.

Complete step-by-step answer:

We have been given that the monthly pocket money of Ravi and Sanjeev are in the ratio 5:7.

So, let Ravi’s pocket money be 5x then Sanjeev’s pocket money will be 7x.

Now, we are also given that their expenditures are in ratio 3:5.

So, let Ravi’s expenditure be 3y then Sanjeev’s expenditure will be 5y.

Now as they both save Rs.80 every month therefore the sum of saving and the expenditure will be their total pocket money.

$ \Rightarrow 5x = 3y + 80$ ……………Equation (1)

and

$7x = 5y + 80$ ………………. Equation (2)

Now, when we subtract Equation (1) from Equation (2), we get,

$2x = 2y$

$ \Rightarrow x = y$……………………... Equation (3)

So, when we put Equation (3) in Equation (1) we get,

$5x = 3x + 80$

$ \Rightarrow 2x = 80$

$ \Rightarrow x = 40$

Now, their pocket money is $5x = 200$ and $7x = 280$.

Hence Ravi’s pocket money is Rs.200 and Sanjeev’s pocket money is Rs.280.

Note: Whenever we face such types of problems the main point to remember is that we need to have a good grasp over linear equations in two variables. In these types of questions, we should always firstly remove the ratio form by assuming some variable and then form linear equations. This helps in getting us the required condition and gets us on the right track to reach the answer.

Complete step-by-step answer:

We have been given that the monthly pocket money of Ravi and Sanjeev are in the ratio 5:7.

So, let Ravi’s pocket money be 5x then Sanjeev’s pocket money will be 7x.

Now, we are also given that their expenditures are in ratio 3:5.

So, let Ravi’s expenditure be 3y then Sanjeev’s expenditure will be 5y.

Now as they both save Rs.80 every month therefore the sum of saving and the expenditure will be their total pocket money.

$ \Rightarrow 5x = 3y + 80$ ……………Equation (1)

and

$7x = 5y + 80$ ………………. Equation (2)

Now, when we subtract Equation (1) from Equation (2), we get,

$2x = 2y$

$ \Rightarrow x = y$……………………... Equation (3)

So, when we put Equation (3) in Equation (1) we get,

$5x = 3x + 80$

$ \Rightarrow 2x = 80$

$ \Rightarrow x = 40$

Now, their pocket money is $5x = 200$ and $7x = 280$.

Hence Ravi’s pocket money is Rs.200 and Sanjeev’s pocket money is Rs.280.

Note: Whenever we face such types of problems the main point to remember is that we need to have a good grasp over linear equations in two variables. In these types of questions, we should always firstly remove the ratio form by assuming some variable and then form linear equations. This helps in getting us the required condition and gets us on the right track to reach the answer.

Last updated date: 20th Sep 2023

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