Question

A man purchased a box full of pencils at the rate of 7 for Rs 9 and sold all for them at the rate of 8 for Rs 11. In this transaction, he gained Rs 10. How many pencils did the box contain?
A) 100
B) 112
C) 114
D) 115

Answer 1

Hint:
We will assume the number of pencils in the box to be \[x\]. Next, we will calculate the cost price of one pencil and the cost price of \[x\] pencils using the given information. Then, we will find the selling price of one pencil and the selling price of \[x\] pencils. Finally, we will find \[x\] using the profit made on this transaction by subtracting obtained cost price from obtained selling price.

Formula used:
Profit \[ = \] Selling Price \[ - \] Cost Price

Complete step by step solution:
It is given that a man has purchased a box full of pencils at the rate of 7 for Rs 9.
This means that the man has spent Rs 9 to buy 7 pencils.
Also, he has sold 8 pencils for Rs 11. On this transaction, he has made a profit of Rs 10.
We are required to find the number of pencils in the box.
Let us assume that the number of pencils in the box is \[x\].
Cost Price of one pencil \[ = \dfrac{9}{7}\]
So, Cost Price of \[x\] pencils \[ = \dfrac{9}{7} \times x\] ……….\[(1)\]
Also, Selling Price of one pencil \[ = \dfrac{{11}}{8}\]
So, Selling Price of \[x\] pencils \[ = \dfrac{{11}}{8} \times x\] ……….\[(2)\]
The man has made a profit of Rs 10 on this transaction.
Substituting the values in the formula Profit \[ = \] Selling Price \[ - \] Cost Price, we get
\[10 = \dfrac{{11x}}{8} - \dfrac{{9x}}{7}\]
We will not take the LCM of the denominators on the RHS. So, the equation becomes
\[ \Rightarrow 10 = \dfrac{{77x - 72x}}{{56}}\]
Multiplying both side by 56, we get
\[ \Rightarrow 560 = 5x\]
Dividing both sides by 5, we get
\[ \Rightarrow x = 112\]
Therefore, the number of pencils in the box is \[112\].

Therefore, the correct answer is option B.

Note:
We can also solve the problem as follows:
Let us suppose that the number of pencils bought \[ = \]LCM\[(7,8) = 56\]
Now, Cost Price of one pencil \[ = \] Total Cost Price \[ \div \] No. of pencils \[ = \dfrac{9}{7}\]
So, Cost Price of 56 pencils \[ = \left( {\dfrac{9}{7} \times 56} \right) = {\rm{Rs}}.72\]
Now, Selling Price of one pencil \[ = \] Total Selling Price \[ \div \] No. of pencils \[ = \dfrac{{11}}{8}\]
So, Selling Price of 56 pencils \[ = \left( {\dfrac{{11}}{8} \times 56} \right) = {\rm{Rs}}.77\]
Amount gained on selling 56 pencils \[ = 77 - 72 = {\rm{Rs}}.5\]
But the man has gained a profit of Rs 10.
This will happen on selling \[\left( {\dfrac{{56}}{5} \times 10} \right) = 112\] pencils.