Question No. 1
A trader sells a 55inch TV set of company X at a profit of 7.5% and a 43 inch TV set of company Y at a gain of 27.5%, making a total profit of Rs.20,500. Had he sold
the TV set of company X at a gain of 12.5% and the other at a gain of 22.5%, he would have gained Rs.2,000 more. What is the cost (in Rs) of the 55 inch TV set of
Company X?
Answers
Answer:
Step-by-step explanation:
Take price of 55 Inch TV be Rsx
And price of 43 Inch TV be Rsy
Now,as per question make the Quadratic Equation :-
0.075x + 0.275y = 20500..(i)
0.125x + 0.225y = 22500..(ii)
Take the L.C.M of 0.275 and 0.225
So that we can eliminate one term.
Therefore L.C.M of 0.275 and 0.225 will be 2.475.
So,As per L.C.M
Multiply equation (i) by 9 and
(ii) by 11...so our next quadratic equation will be
0.675x + 2.475y = 184100
1.375x + 2.475y = 247500
-. -. -
______________________
(-0.7x) = (-63000)
Term y will get eliminated
Therefore X= 63000/0.7=90000rs
So Cost of 55 inch TV of company X will be 90000rs.
Given : 55 inch TV x company 7.5% Gain + 43 inch TV Y company 27.5% Gain => total Profit = 20500 if 55 inch at 12.5% & 43 inch at 22.5 % then profit increased by 2000
To find : cost (in Rs) of the 55 inch TV set of Company X
Solution:
Let say 55 inch TV Cost = Rs 1000X
7.5 % Profit = (7.5/100)1000X = 75X Rs
Let say 43 inch TV Cost = Rs 1000Y
27.5 % Profit = (27.5/100)1000Y = 275Y Rs
75X + 275Y = 20500
=> 3X + 11Y = 820 Eq1
gain of 12.5% at 55 inch TV = 125X
gain of 22.5% at 43 inch TV = 225Y
125X + 225Y = 20500 + 2000
=> 5X + 9Y = 900 Eq2
11 * Eq2 - 9 * Eq1
=> 55X - 27X = 9900 - 7380
=> 28X = 2520
=> X = 90
=> 1000X = 90000
cost (in Rs) of the 55 inch TV set of Company X = Rs 90000
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