Question 1086296: The monthly pocket money of Ravi and Sanjiv are in the ratio 5 to 7 their expenditures are in the ratio 3 to 5 if each saves rupees 80 every month. Find their monthly pocket money.
My solution
Let the monthly pocket money of Ravi 5X and Sanjiv be 7y
Their expenditures be 3x and 5y
According to question
5x-3x=80
7y-5y=80
I don't know whether it is correct or wrong please tell me the correct answer
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! their pocket money is in the ratio of 5 to 7.
their expenses are in the ratio of 3 to 5.
they each save 80 rupees each month.
your formula would get:
you would get 2x = 80 which results in x = 40.
you would get 2y = 80 which results in y = 40.
i'm not sure what x or y would represent.
you actually have 4 variables that need to be solved for.
they are ravi monthly pocket money and sanjiv pocket money and ravi expenditures and sanjiv expenditures.
bottom line is it doesn't look right.
i tried an alternate approach and i got an answer that makes sense.
this is what i did.
your problem is:
The monthly pocket money of Ravi and Sanjiv are in the ratio of 5 to 7 and their expenditures are in the ratio of 3 to 5.
if each saves rupees 80 every month. Find their monthly pocket money.
let a equal the pocket money that ravi gets and let b equal the pocket money that sanjiv gets.
the ratio becomes a/b = 5/7
let c equal the expenditures of ravi and let d equal the expenditures of sanjiv.
the ratio becomes c/d = 3/5
from a/b = 5/7, you can solve for a to get a = 5b/7
from c/d = 3/5, you can solve for c to get c = 3d/5
the formula for savings is savings = pocket money minus expenditures.
you know that both ravi and sanjim save 80 rupees per month.
you get a - c = 80 and you get b - d = 80
since they are both equal to 80, then you get a - c = b - d
since a = 5b/7 and c = 3d/5, then you get:
5b/7 - 3d/5 = b - d
multiply both sides of this equation by 35 and you get:
25b - 21d = 35b - 35d
subtract 25b from both sides of this equation and add 35d to both sides of this equation and you get:
35d - 21d = 35b - 25b
simplify to get:
14d = 10b
solve for b to get:
b = 1.4d
from b - d = 80, replace b with 1.4d and you get:
1.4d - d = 80
simplify to get .4d = 80
solve for d to get d = 200
when d = 200, then b - d = 80 becomes b - 200 = 80.
this results in b = 280.
you now have b = 280 and d = 200
you know that a = 5b/7 and c = 3d/5, so you get:
a = (5 * 280) / 7 = 200
c = (3 * 200) / 5 = 120
you now have:
a = 200 = ravi monthly pocket money
b = 280 = sanjiv monthly pocket money
c = 120 = ravi monthly expenditures
d = 200 = sanjiv monthly expenditures
you know that ravi and sanjiv both save 80 rupees per month.
for ravi, this becomes 200 - 120 = 80
for sanjiv, this becomes 280 - 200 = 80
solution looks good.
rajiv monthly pocket money is equal to 200 rupees.
sanjiv monthly pocket money is equal to 280 rupees.
the pocket money ratio is a / b = 200 / 280 = 5 / 7.
the expenditure ratio is c / d = 120 / 200 = 3 / 5.
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