the monthly income of a and b are in the ratio4:3 and their monthly savings are in the ratio 9:5.if each spends rs 3500 per month find their monthly savings
Answers
see in attachment
Let monthly incomes of A and B be x&y
Given
y
x
=
3
4
⇒x=
3
4y
Income =expenditure+savings
Let their expenditures be A and B
x=A+1500
y=B+1500
A=x−1500B=y−1500
Given
B
A
=
9
13
y−1500
x−1500
=
9
13
y−1500
3
4y
−1500
=
9
13
3(y−1500)
4y−4500
=
9
13
3(4y−4500)=13(y−1500)
12y−13500=13y−19500
y=19500−13500
=6000
x=
3
4×4
=
3
4×6000
4×2000=8000
∴ Monthly incomes of A and B are 8000&6000
Step-by-step explanation:
Given :-
The monthly income of a and b are in the ratio 4:3 and their monthly savings are in the ratio 9:5 and each spends Rs. 3500 per month .
To find :-
Find their monthly savings ?
Solution :-
The ratio of monthly incomes of a and b = 4:3
Let they be 4X and 3X
The monthly income of a = Rs. 4X
The monthly income of b = Rs. 3X
The ratio of monthly savings of a and b = 9:5
Let they be 9Y and 5Y
The monthly saving of a = Rs. 9Y
The monthly saving of b = Rs. 5Y
We know that
Income = Saving + Spending
=> Spending = Income - Saving
The monthly Spending of a = 4X-9Y
According to the given problem
The monthly spending money of a = Rs. 3500
=> 4X-9Y = 3500 ---------(1)
The monthly Spending of b = 3X-5Y
According to the given problem
The monthly spending money of b = Rs. 3500
=> 3X-5Y = 3500 ----------(2)
=> 3X = 3500+5Y
=> X = (3500+5Y)/3 --------(3)
On substituting the value of X im (1) then
=>4[(3500+5Y)/3]-9Y = 3500
=> [(14000+20Y)/3]-9Y = 3500
=> (14000+20Y-27Y)/3 = 3500
=> (14000-7Y)/3 = 3500
=> 14000-7Y = 3500×3
=> 14000-7Y = 10500
=> 7Y = 14000-10500
=> 7Y = 3500
=> Y = 3500/7
=> Y = 500
On substituting the value of Y in (3) then
=>X = (3500+5(500))/3
=> X = (3500+2500)/3
=> X = 6000/3
=> X = 2000
The monthly saving of a = 9Y
=> 9×500 = Rs. 4500
The monthly saving of b = 5Y
=> 5×500
=> Rs. 2500
Answer:-
The monthly saving of a is Rs. 4500
The monthly saving of b is Rs. 2500
Check:-
Monthly income of a = 4X
= 4×2000 = Rs. 8000
Monthly income of b = 3X
= 3×2000 = Rs. 6000
The monthly saving of a = 9Y
=> 9×500 = Rs. 4500
The monthly saving of b = 5Y
=> 5×500
=> Rs. 2500
The monthly Spending of a
= 8000-4500
= 3500
and
The monthly Spending of b
= 6000-2500
=3500
Verified the given relations in the given problem.