The monthly income of A and B are in the ratio 7 : 5 and their expenditures are in the ratio 3 : 2. If each saves Rs. 1500 per month, find their monthly incomes.
Answers
Question :-
▪ The monthly income of A and B are in the ratio 7 : 5 and their expenditures are in the ratio 3 : 2 . If each saves Rs.1500 per month , find their monthly incomes.
Solution :-
• ratio of income of A and B = 7 : 5
• ratio of their expenditures = 3 : 2
each of them saves Rs. 1500
income = expenditures + saving
¤ let the income of A and B be 7x and 5x respectively ....
¤ and the expenditure of A and B be 3y and 2y respectively...
☆ income - expenditure = saving
for A:-
7x - 3y = 1500 ----------> equation ( 1 )
for B :-
5x - 2y = 1500 ----------> equation ( 2 )
● multiplying eqn (1) with 2 and eqn (2) with 3
thus, we get simultaneous equation in two variables.
( 7x - 3y = 1500 ) × 2
( 5x - 2y = 1500) × 3
the equations are---
14x - 6y = 3000 ------> equation (3)
15x - 6y = 4500 -------> equation (4)
subtracting eqn (3) from eqn (4),
15x - 6y = 4500
14x - 6y = 3000
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x = 1500
substituting the value of x in equation (2),
5x - 2y = 1500
=》5 (1500) - 2y = 1500
=》2y = 7500 - 1500
=》 2y = 6000
=》 y = 3000
thus,,
monthly income of A = 7x = 7×1500 = Rs. 10,500
monthly income of B = 5x = 5 ×1500 = Rs. 7,500
expenditure of A = 3y = 3× 3000 = Rs. 9000
expenditure of B = 2y = 2× 3000 = Rs. 6000
☆HoPE iT hELpS you
Given:-
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- Ratio of monthly income of A : B = 7 : 5
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- Ratio of expenditure per month =3 : 2
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- Savings = Rs. 1500
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To find:-
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- monthly income of both A and B???
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Solutions:-
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Let the monthly income of A = 7x
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Let the monthly income of B = 5x
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Let the ratio of expenditure per monthly be 3y and 2y
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Monthly saving of A = 7x - 3y
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Monthly saving of B = 5x - 2y
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Acc. to the question :-
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7x - 3y = 1500 ........(i)
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5x - 2y = 1500 .........(ii)
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- Multiplying Eq. (i) by 2 and Eq. (ii) by 3
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14x - 6y = 3000 ........(iii)
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15x - 6y = 4500 .........(iv)
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- Subtracting Eq. (iii) from Eq. (iv)
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15x - 6y - ( 14x - 6y ) = 4500 - 3000
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15x - 6y - 14x + 6y = 4500 - 3000
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x = 1500
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- putting value of x in monthly income
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A's income = 7x = 7 × 1500 = Rs.10500
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B's income = 5x = 5 × 1500 = Rs. 7500
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Answer :-
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- A's and B's monthly income is Rs.10500 and Rs.7500 respectively
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