Question

In a stationary shop, the cost of 3 geometry boxes exceeds the price of 2 pens by Rs. 2. Also, the total price of 7 geometry boxes and 3 pens is Rs. 43. Find the cost of one geometry box and pen.
(a). Rs. 6 and Rs. 8
(b). Rs. 4 and Rs. 5
(c). Rs. 3 and Rs. 4
(d). Rs. 2 and Rs. 5

Answer 1

Hint: If the price of one geometry box is Rs. x and one pen is Rs. y, according to the given conditions try to make two equations of x and y. Then solve and find out the values of x and y.

Complete step-by-step answer:

Let us assume that the cost of one geometry box is Rs. x.
Cost of one pen is Rs. y.
It is given in the question that, total price of 7 geometry boxes and 3 pens is Rs. 43.
If the price of one geometry box is Rs. x, price of 7 geometry boxes will be Rs. 7x.
If the price of one pen is Rs. y, price of 3 pens will be Rs. 3y.
According to the question,
$7x+3y=43......(1)$
Another condition is the cost of 3 geometry boxes exceeds the price of 2 pens by Rs. 2.
If the price of one geometry box is Rs. x, then the price of 3 geometry boxes will be Rs. 3x.
Similarly, the price of 2 pens will be Rs. 2y.
According to the question,
$3x-2y=2.....(2)$
Now, we will solve equation (1) and (2) to get the value of x and y.
We will multiply equation (1) by 2 and equation (2) by 3.
$14x+6y=86......(3)$
$9x-6y=6.....(4)$
Now, we will add equation (3) and (4). Therefore,
$\left( 14x+6y \right)+\left( 9x-6y \right)=86+6$
By cancelling out the opposite terms we will get,
$\Rightarrow 23x=92$
By dividing both sides of the equation by 23 we will get,
$\Rightarrow x=\dfrac{92}{23}$
$\Rightarrow x=4$
Now, we will put the value of x in equation (2) to get the value of y.
$\left( 3\times 4 \right)-2y=2$
$\Rightarrow 12-2y=2$
Take 12 from left hand side to right hand side,
$\Rightarrow -2y=2-12$
By dividing both sides by -2 we will get,
$\Rightarrow y=\dfrac{-10}{-2}$
$\Rightarrow y=5$
Hence, the price of one geometry box is Rs. 4 and price of one pen is Rs. 5.
Therefore, option (b) is correct.

Note: Alternatively we can find out the answer just by cross checking the options. Here we can clearly see that only option (b) is satisfying both conditions. Therefore, option (b) is correct.