Question

Raju sold a bicycle to Amit of 8% profit. Amit repaired it, spending Rs. 54. Then he sold the bicycle to Nikhil for Rs. 1134 with no loss and profit. Find the cost price of the bicycle for which Raju purchased it.

Answer 1

Hint: We will first assume the cost price of the bicycle for Raju to be Rs. x. Now, applying 8% profit on it, we will get the selling price for Raju and cost price for Amit and now adding 54 to it and substituting it equal to 1134 will give us the answer.

Complete step-by-step solution:
Let us assume that the cost price for which Raju bought the cycle in the first place is Rs. x
Now, since he sold it to Amit at a profit of 8%.
So, profit = 8% of cost price.
$ \Rightarrow $Profit = $\dfrac{8}{{100}}x = 0.08x$
Now we will use the following formula:-
$ \Rightarrow $Selling Price = Cost Price + Profit
Putting the values from above, we will then obtain:-
$ \Rightarrow $Selling Price = x + 0.08x = 1.08x
Now, this selling price for Raju is the cost price for Amit.
So, cost price for Amit = Rs. 1.08x
Now, Amit also spent Rs. 54 on its reparing.
So, if we add both the cost price and the money spent for repairing for Amit, we will get:-
Cost of bicycle for Amit = Rs. (1.08x + 54)
Now, Amit sold it to Nikhil with no loss an no profit.
Therefore, the selling price for Amit = Rs. (1.08x + 54)
But it is given to be equal to Rs. 1134.
$ \Rightarrow Rs.\left( {1.08x + 54} \right) = Rs.1134$
Since we have the unit rupees on both sides, we can cut it off to get:-
$ \Rightarrow 1.08x + 54 = 1134$
Taking 54 from addition in LHS to subtraction in RHS, we will then obtain:-
$ \Rightarrow 1.08x = 1134 - 54$
Simplifying the calculations on the RHS of above expression, we will get:-
$ \Rightarrow 1.08x = 1080$
Taking 1.08 from multiplication in LHS to division in RHS so that we get:-
$ \Rightarrow x = \dfrac{{1080}}{{1.08}}$
We can rewrite the above expression as:-
$ \Rightarrow x = \dfrac{{1080}}{{108}} \times 100$
Simplifying the calculations above, we will get:-
$ \Rightarrow x = 10 \times 100$
Simplifying the calculations above further, we will get:-
$ \Rightarrow x = 1000$

$\therefore $ Raju bought the cycle for Rs. 1000.

Note: The students must note that they must mention the cost price for which person whenever they are talking about the cost price because the cost price for Amit is the selling price for Raju and so much more like this. Therefore, we must mention it so that it is easier for us to understand.
The students can also assume the selling price for Raju to be Rs. x and then find the cost price by subtracting the profit from it. DO the further using the same and we will get the value of x as according to it.