The ratio of income of a and b is 5:4 and their expenditure is as 3:2. If at the end of the year, each saves rs. 800, then the income of a is
Answers
Answer: 2000 and 1600
Step-by-step explanation:
The ratio of incomes of a and b is 5:4
∴ Let their incomes be 5x and 4x
The ratio of their expenses is 3:2
∴ Let their expenses be 3y and 2y
Each person saves 800
savings = income - expenses
5x - 3y = 800 ..... 1
4x - 2y = 800 ..... 2
To use the method of elimination
equation 1 can be rewritten as 10x - 6y = 1600 by multiplying all the terms by 2
equation 2 can be rewritten as 12x - 6y = 2400 by multiplying all the terms by 3
Subtracting equation 1 from 2
(12x - 6y) - (10x - 6y) = 2400 - 1600
12x - 6y - 10x + 6y = 800
2x = 800
x = 400
Hence the income of the two persons = 5x = 5 X 400 = 2000 and 4x = 4 X 400 = 1600
Answer:
Step-by-step explanation:
Let their income be x and expenditure be y.
A
′
s income =5x
B
′
s income =4x
A
′
s expenditure =3y
B
′
s expenditure =2y
Save money =Rs.1600
⇒ Income - expenditure = saves
⇒ 5x−3y=1600 ---- ( 1 )
⇒ 4x−2y=1600 --- ( 2 )
Multiply equation ( 1 ) by 2 and equation ( 2 ) by 3, we get,
⇒ 10x−6y=3200 ---- ( 3 )
⇒ 12x−6y=4800 ---- ( 4 )
By subtracting ( 4 ) from ( 1 ) we get,
⇒ x=800
⇒ Income of A=5x=5×800=Rs.4000
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