The monthly incomes of A and B are in the ratio of 5 : 4 and their monthly expenditures are in the ratio of 7 : 5. If each saves Rs. 3000 per month, find the monthly income of each.
Answers
Let x be the ratio of income then,
The income of A=5x and
The income of B=4x
Let y be the ratio of expenditure then,
The expenditure of A=7y
The expenditure of B=5y
Savings of A=Savings of B=3000
According to question
5x-7y=3000…..(1)
4x-5y=3000…..(2)
(1)-(2)
x-2y=0=>x=2y
From(2)
8y-5y=3000
3y=3000
y=1000
x=2×1000=2000
Therefore the monthly income of A=5×2000
=₹10,000
And the monthly income of B=4×2000= 8000
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Answer:
the monthly income of A is Rs. 10000 and monthly income of B is 8000.
Step-by-step explanation:
The monthly income of A and B are in the ratio of 5, ratio 4
Let the rational between incomes of A and B be x. Thus the income of A is 5x and income if B is 4x
Their monthly expenditure are in the ratio of 7, ratio 5.
Let the rational between expenditure if A and B be y. Thus, the expenditure of A is 7y and expenditure if B is 5y
We know Savings = Income - expenditure
The respective Savings of A and B are Rs. 3000. Therefore savings of A
5x - 7y = 3000…..
5x = 3000 + 7y..Eq…1
The savings of B
4x - 5y = 3000
4x = 3000 + 5y…..Eq..2
Now multiply Eq 1 wuth 4 and Eq 2 with 5 to equate
20x = 12000 + 28y.. Eq…3
20x= 15000 + 25y…Eq..4
Now square Eq..3 with Eq…
12000 + 28y = 15000 + 25y
28y - 25y = 15000 - 12000
3y = 3000
y = 3000/3
y = 1000
Now substituting the value of y in Eq…2 to derive value of x
4x = 3000 + 5y
4x = 3000 + 5 × 1000
4x = 3000 + 5000
4x = 8000
x = 8000 / 4
x = 2000
The rational is 2000. Therefore the monthly income of A abd B are
A = 5x = 5 × 2000 = Rs.10,000
B = 4x = 4 × 2000 = Rs. 8,000
the monthly income of A is Rs. 10000 and monthly income of B is 8000.