Mr. Ramesh bought two watches which together cost him Rs.440. He sold ...
80/100 * x = 140/100 * y
x = 7/4y
x + y = 440
7/4 y + y = 440
y = 160 ; x = 280
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Mr. Ramesh bought two watches which together cost him Rs.440. He sold ...
To solve this problem, we need to find the cost price (CP) and selling price (SP) for each watch.
Let's assume the cost price of the first watch is x. Since Mr. Ramesh sold this watch at a loss of 20%, the selling price of the first watch is 0.8x.
Now, let's assume the cost price of the second watch is y. Since Mr. Ramesh sold this watch at a gain of 40%, the selling price of the second watch is 1.4y.
We know that the total cost of both watches is Rs. 440. So we can write the following equation:
x + y = 440
We also know that the selling prices of both watches are the same. So we can write the following equation:
0.8x = 1.4y
Now, let's analyze the given quantities:
Quantity I: SP and CP of one of the watches sold at a loss of 20%
In this case, we need to find the selling price and cost price for one of the watches sold at a loss of 20%. This means we need to find the value of x.
Quantity II: SP and CP of one of the watches sold at a profit of 40%
In this case, we need to find the selling price and cost price for one of the watches sold at a profit of 40%. This means we need to find the value of y.
To determine whether Quantity I or Quantity II is greater, we need to solve the equations to find the values of x and y.
From equation 2, we can rewrite it as:
x = 1.75y
Substituting this value of x into equation 1, we get:
1.75y + y = 440
2.75y = 440
y = 440/2.75
y = 160
Now, substituting the value of y into equation 2, we get:
x = 1.75(160)
x = 280
So the cost price and selling price for one of the watches sold at a loss of 20% are:
CP = Rs. 280
SP = 0.8(280) = Rs. 224
Therefore, Quantity I is 224.
Since we have found the values of x and y, we can also find the selling price and cost price for one of the watches sold at a profit of 40%:
CP = Rs. 160
SP = 1.4(160) = Rs. 224
Therefore, Quantity II is also 224.
Hence, the answer is:
a) Quantity I = Quantity II = 224.