if the C.P. of an umbrella be decreased by Rs.60, there is a profit of 7.5% at present instead of a loss of 5% of the past. What was the C.P. of the umbrella at past.? [Please answer the question using Pure Arithmetic.]
Let's assume the cost price (C.P.) of the umbrella at present is 'x'.
According to the given information, if the C.P. is decreased by Rs. 60, there is a profit of 7.5% instead of a loss of 5% in the past.
So, the selling price (S.P.) at present will be 107.5% of the reduced C.P.
Therefore, the S.P. at present will be 107.5% of (x-60).
S.P. = 107.5% of (x-60)
S.P. = (107.5/100) * (x-60)
S.P. = (215/200) * (x-60)
S.P. = (43/40) * (x-60)
Now, let's set up the equation for the past scenario, where there was a loss of 5%.
The S.P. in the past would be 95% of the original C.P.
Therefore, the S.P. in the past would be 95% of x.
S.P. = 95% of x
S.P. = (95/100) * x
S.P. = (19/20) * x
Now, we can equate the two S.P. equations to find the value of x, which represents the original C.P.
(43/40) * (x-60) = (19/20) * x
Multiply both sides by 40 to eliminate the denominators:
43 * (x-60) = 19 * 20 * x
43x - 43 * 60 = 380x
Move the terms containing x to one side and the constant terms to the other side:
380x - 43x = 43 * 60
337x = 43 * 60
Divide both sides by 337 to solve for x:
x = (43 * 60) / 337
x ≈ 7.653
Therefore, the C.P. of the umbrella in the past was approximately Rs. 7.653.
To find out the cost price (C.P.) of the umbrella in the past, we need to consider the given information:
1. If the C.P. of the umbrella is decreased by Rs. 60, there is a profit of 7.5% at present.
2. In the past, there was a loss of 5%.
Let's assume the C.P. of the umbrella in the past was 'x' Rupees.
According to the given information, if the C.P. of the umbrella is decreased by Rs. 60, the profit at present is 7.5%. Mathematically, we can express this as:
New C.P. = x - 60
Profit % = 7.5%
Using the formula for profit percentage, we can say:
Profit % = [(Profit / C.P.) * 100]
As the profit percentage is expressed as a positive value, we need to consider the magnitude of the loss percentage, which is 5% (expressed as a negative value due to a loss).
So, the loss percentage in the past is |-5%| = 5%.
Using the formula for loss percentage, we can say:
Loss % = [(Loss / C.P.) * 100]
Now, let's equate the profit and loss percentages to find the C.P. of the umbrella in the past.
Profit % = Loss %
7.5% = 5%
[(Profit / New C.P.) * 100] = [(Loss / C.P) * 100]
[(Profit / (x - 60)) * 100] = [(Loss / x) * 100]
Cross-multiplying, we get:
(7.5 / 100) * x = (5 / 100) * (x - 60)
Simplifying further:
0.075x = 0.05x - 3
0.075x - 0.05x = -3
0.025x = -3
x = -3 / 0.025
x = -120
Hence, the C.P. of the umbrella in the past was Rs. 120.