Answer

Verified

449.1k+ views

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.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

One cusec is equal to how many liters class 8 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

How many crores make 10 million class 7 maths CBSE

Change the following sentences into negative and interrogative class 10 english CBSE