Question

A person bought two clocks. The cost price of one of them exceeds by \[\dfrac{1}{4}\] the price of the other. He sold the costlier clock to the dealer at a gain of 10% and the other at 7.5% and thus got Rs 98 in all as SP. Find the total cost price of two clocks.

Answer 1

Hint:We know that Gain=SP-CP
So, we will first take the cost price of one clock a random number x.
Then by given condition we can find the cost price of the other clock.
As the gain % for both the clocks are given, we can easily find the total Sp in terms of x.
Equating the total SP in terms of x with the given value, we can find the value of x from that.
The cost price of the other clock and total cost price we can calculate from that.

Complete step-by-step answer:
Let, the cost price of one clock is Rs. x.
The cost price of one of them exceeds by \[\dfrac{1}{4}\] the price of the other.
Then the cost price of the other clock is \[x - x \times \dfrac{1}{4} = Rs.\dfrac{{3x}}{4}\]
It is given that the person sold the costlier clock to the dealer at a gain of 10% and the other at 7.5%.
So the costlier clock that is the first clock is sold at a gain 10%,
So the SP of the first clock is \[ = x + x \times \dfrac{{10}}{{100}}\]\[ = x + \dfrac{x}{{10}}\]\[ = \dfrac{{11x}}{{10}}\]
The other clock is sold at a gain 7.5%,
So the SP of the second clock is \[ = \dfrac{{3x}}{4} + \dfrac{{3x}}{4} \times \dfrac{{7.5}}{{100}}\]
On solving the above equation we get,
\[\dfrac{{3x}}{4} + \dfrac{{3x}}{4} \times \dfrac{{7.5}}{{100}}\]\[ = \dfrac{{3x}}{4} + \dfrac{{3x}}{4} \times \dfrac{3}{{40}}\]
\[ = \dfrac{{120x + 9x}}{{160}}\]
\[ = \dfrac{{129x}}{{160}}\]
The total Selling Price of both the clocks is \[ = \dfrac{{11x}}{{10}} + \dfrac{{129x}}{{160}}\]
\[ = \dfrac{{176x + 129x}}{{160}}\]
On solving the above the equation we get\[ = \dfrac{{305x}}{{160}}\]
It is given that the person got Rs 98 in all as a selling Price.
Equating these two values we get,
\[\dfrac{{305x}}{{160}} = 98\]
Let us solve the above equation for x, we get
\[x = \dfrac{{98 \times 160}}{{305}}\]
\[x = 51.40\]
The cost price of the second clock is \[ = 51.40 \times \dfrac{3}{4}\]\[ = 38.56\]
Thus the cost price of the first clock is Rs.51.40
Thus the cost price of the second clock is Rs.38.56.
Therefore,
The total cost price of the two clocks is Rs.(51.40+38.56)= Rs.89.95.

The total cost price of two clocks is Rs.89.95.

Note:Here we use the formula Selling Price=Cost Price +Cost Price .Gain%. Here it is given that the cost price of one of them exceeds by \[\dfrac{1}{4}\] the price of the other. In other words we can say that one clock is less by \[\dfrac{1}{4}\] the price of the other.