Question

the monthly pocket money of Ravi and Sanjeev are in the ratio 5:7 their expenditure ratio is 9:13 if each saves rupees 40 find their pocket money

Pls give the answer step by step pls

Answer 1

Let :-

• The monthly pocket money for Ravi = 5x
• The monthly pocket money for Sanjeev = 7x
• The monthly expenditure for Ravi = 9y
• The monthly expenditure for Sanjeev = 13y

Given :-

• Ratio of pocket money for them = 5 : 7
• Ratio of expenditure money for them = 9 : 13
• Monthly savings for Ravi = ₹ 40
• Monthly savings for Sanjeev = ₹ 40

To Find :-

• Monthly pocket money for Ravi = ?
• Monthly pocket money for Sanjeev = ?

Solution :-

• To calculate their monthly pocket money at first we have to set up equation as per the given clue in the question. Then solve the equation. By solving the equation we can easily find the out the monthly pocket money of Ravi and Sanjeev.

Calculation for Ravi :-

• Monthly savings = ₹ 40
• Monthly pocket money = 5x
• Monthly expenditure = 9y

⇢ Pocket money - Expenditure = Savings

⇢ 5x - 9y = 40----------(i)

Calculation for Sanjeev :-

• Monthly savings = ₹ 40
• Monthly pocket money = 7x
• Monthly expenditure = 13y

⇢ Pocket money - Expenditure = Savings

⇢ 7x - 13y = 40----------(ii)

• In equation (i) multiplying by (7) and in equation (ii) multiplying by (5) then subtract.

⇢ 35x - 63y = 280--------(iii)

⇢ 35x - 65y = 200--------(iv)

• By subtracting eq (iii) and (iv) we get :-]

⇢ 2y = 80 ⇢ y = 40

• Putting the value of y = 40 in eq (i) :-]

⇢ 5x - 9y = 40

⇢ 5x - 9(40) = 40

⇢ 5x - 360 = 40

⇢ 5x = 360 + 40

⇢ 5x = 400 ⇢ x = 80

Hence,

⇢ Monthly pocket money for Ravi = 5x

⇢ Monthly pocket money = 5 × 80

⇢ Monthly pocket money = ₹ 400

⇢ Monthly pocket money for Sanjeev = 7x

⇢ Monthly pocket money = 7 × 80

⇢ Monthly pocket money = ₹ 560

Answer 2

Answer:

$\sf\tt\large{\green {\underline {\underline{⚘\;Question:}}}}$

• The monthly pocket money of Ravi and Sanjeev are in the ratio 5:7 their expenditure ratio is 9:13.If each saves rupees 40.Find their pocket money.

$\sf\tt\large{\red {\underline {\underline{⚘\;Answer:}}}}$

• The monthly pocket money of Ravi =$400
• The monthly pocket money of Sanjeev =$560.

$\sf\tt\large{\blue {\underline {\underline{⚘\;Given: }}}}$

• The monthly pocket money of Ravi and Sanjeev are in ratio 5:7 their expenditure ratio is 9:13.If each saves $40.

$\sf\tt\large{\red {\underline {\underline{⚘\;To find:}}}}$

• Here we should find the pocket money of Ravi and Sanjeev.

$\sf\tt\large{\green {\underline {\underline{⚘\;Solution:}}}}$

$\sf\tt\large{\green {\underline {\underline{⚘\;Consider:}}}}$

$\sf\tt\large{\red {\underline {\underline{⚘\;Case (i):}}}}$

• In the case of Ravi .

• If we want to get the answer to this question we should convert the given question clues into a equation.Then we can solve.
• Here,

• Money savings =$40,Monthly pocket money =5m,Monthly expenditure is =9n
• Then, here we get the equation that is

$5m - 9n = 40$

$\sf\tt\large{\green {\underline {\underline{⚘\;Case (ii):}}}}$

• In the case of Sanjeev

• Money savings =$40,Monthly pocket money =7m,Monthly expenditure =13n
• Then we get the equation that is,

$7m - 13n = 40$

Let,

• Here we should change something else that is we should multiply the equation i in 7 and equation (ii) in 5
• Then we get that,

$35m - 63n = 280 - - - - (i)$

$35m - 65n =200 - - - - (ii)$

Now,

• By subtracting two equations we get that,

• $+ 2n = 80$
• $n = \frac{80}{2} = 40$

Now,

• Putting the value of n in equation 2 we get that,

• $7m - 13n = 40$
• 7m-13 (40)=40
• 7m-520=40
• 7m=40+520
• 7m=560
• m=560/7
• m=80.

$\sf\tt\large{\red {\underline {\underline{⚘\;Therefore:}}}}$

1. Monthly pocket money of Ravi =5m=5×80=$400
2. Monthly pocket money of Sanjeev =7m=7×80=$560.

$\large{\bf{\green{\mathfrak{\dag{\underline{\underline{Which \;is\;the \;required\; Answer}}}}}}}$

Hope it helps u mate .

Thank you .