1. The incomes of A and B are in the ratio 3:2 and their expenditures in the ratio 5:3. If each saves *1500, then B's income is (a) 6000 (c) 3000 (b) *4700 (d) 7500
Answers
Answer:
Option (a) 6000
Step-by-step explanation:
Savings=Income-Expenses
A...1500=3x−5y
B...1500=2x−3y
Solving both the equations, we get,
x=3000
Therefore B's savings =2x=2×3000=Rs.6000
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Answer:
Option (a)
Step-by-step explanation:
Given :-
The incomes of A and B are in the ratio 3:2 .
Their expenditures in the ratio 5:3.
Savings of A and B is Rs. 1500 each .
To find :-
B's income
Solution :-
Given that
The ratio of incomes of A and B = 3:2
Let they be Rs. 3X and Rs. 2X
Income of A = Rs. 3X
Income of B = Rs. 2X
Given that
The expenditure of A and B = 5:3
Let they be Rs. 5Y and Rs. 3Y
The expenditure of A = Rs. 5Y
The expenditure of B = Rs. 3Y
Savings of A and B = Rs. 1500
We know that
Saving = Income - Expenditure
Savings of A = 3X-5Y = 1500 --------(1)
Savings of B = 2X-3Y = 1500 ---------(2)
On multiplying (1) with 2 then it becomes
6X-10Y = 3000 --------------(3)
On multiplying (2) with 3 then it becomes
6X-9Y = 4500 ---------------(4)
On subtracting (3) from (4) then
6X-9Y = 4500
6X-10Y = 3000
(-)
_____________
0 + Y = 1500
_____________
Therefore, Y = Rs. 1500
On substituting the value of Y in (1) then
3X -5(1500) = 1500
=> 3X -7500 = 1500
=> 3X = 1500+7500
=> 3X = 9000
=> X = 9000/3
=> X = 3000
Therefore, X = Rs. 3000
Income of B = Rs. 2X
= Rs. 2(3000)
= Rs. 6000
Answer :-
The income of B is Rs. 6000
Check :-
We have,
X = Rs. 3000
Y = Rs. 1500
A's income = 3X = 3(3000) = Rs. 9000
A's expenditure = 5Y = 5(1500) = Rs. 7500
A's saving = 9000-7500 = Rs. 1500
B's income = 2X = 2(3000) = Rs. 6000
B's expenditure = 3Y = 3(1500) = Rs. 4500
B's saving = 6000-4500 = Rs. 1500
Verified the given relations in the given problem.
Used formulae :-
→ Saving = Income - Expenditure