the monthly income of a and b are in the ratio of 4:5 and their monthly expenses are in the ratio of 11:15, is each of them saves rs.2000 find the income of a
Answers
Step-by-step explanation:
Given :-
The monthly incomes of a and b are in the ratio of 4:5.
Their monthly expenses are in the ratio of 11:15.
Each of them saves Rs.2000 .
To find :-
The income of a .
Solution :-
Given that
The ratio of monthly incomes of a and b
= 4:5
Let they be Rs. 4X and Rs. 5X
The income of a = Rs. 4X
The income of b = Rs. 5X
The ratio of monthly expenses of a and b = 11:15
Let they be Rs. 11Y and Rs. 15Y
The expenses of a = Rs. 11Y
The expenses of b = Rs. 15Y
We know that
Saving = Income - Expenses
The saving of a = Rs. 2000
=> 4X - 11Y = 2000 -----------(1)
and
The Saving of b = Rs. 2000
=> 5X-15Y = 2000
=> 5(X-3Y) = 2000
=> X-3Y = 2000/5
=> X-3Y = 400 -------------(2)
On multiplying (2) with 4 then it becomes
=> 4X-12Y = 1600 ---------(3)
On subtracting (3) from (1) then
4X-11Y = 2000
4X-12Y = 1600
(-)
____________
0 + Y = 400
____________
Therefore, Y = Rs. 400
On substituting the value of Y in (2) then
X-3(400) = 400
=> X -1200 = 400
=> X = 400+1200
=> X = 1600
Therefore, X = Rs. 1600
Now,
Income of a = Rs.4X
=> Rs. 4(1600)
=> Rs. 6400
Income of a = Rs. 6400
Answer:-
The income of a is Rs. 6400
Check:-
We have, X = Rs. 1600 and Y = Rs.400
Income of a = Rs. 6400
Expenses of a = Rs. 11Y
= 11(400)
= Rs. 4400
Saving of a = 6400-4400
= Rs. 2000
and
Income of b = Rs.5X
= 5(1600)
= Rs. 8000
Expenses of b = Rs. 15Y
= 15(400)
= Rs. 6000
Saving of b = 8000-6000
= Rs. 2000
They save Rs. 2000 each.
Verified the given relations in the given problem.
Used formulae:-
→ Saving = Income - Expenses