Question

Seventy-five ball pens cost Rs 637.50. Find the price of 23 ball pens. How many pens can be bought for Rs 800 and how much money will be left?

Answer 1

Hint: To solve this problem, we will assign a variable x for the price of one ball pen. We will then use the fact that the cost of seventy-five ball pens is Rs 637.50 to find the cost of one ball pen and then multiply this with 23 to get the price of 23 ball pens. We will then use the information obtained by solving the first sub-part of the problem in addition to the unitary method to find the number of pens that can be bought for Rs 800.

Complete step-by-step answer:

To solve this problem, we know that the cost of seventy-five ball pens is Rs 637.50. Let x be the cost of one ball pen. Thus, we have,
75x = 637.5
x = 8.5
Thus, the cost of one ball pen is Rs 8.5.
Thus, the cost of 23 ball pens is 8.5 $\times$ 23 = 195.5.
Hence, the cost of 23 ball pens is Rs 195.5.
Now, let’s assume that we need y pens for Rs 800. We know that one pen costs Rs 8.5, thus y pens would cost 8.5y. Since, the cost is given as Rs 800, we have to equate this to 8.5y to get the value of y. Thus, we have,
8.5y = 800
y = 94.117
Since, this is not an integer, we have to round this number (since, pens are bought as a whole and not as fractions). Hence, 94 pens can be bought for Rs 800.
Now, the cost of 94 pens is 8.5 $\times$ 94 = 799. Thus, money left is 800 – 1 = Rs 1.

Note: A simpler way to solve is by using the formula given by ${\displaystyle \frac{637.5}{75}}\times 23$ = 195.5. That is, we simply divide the total cost of the known price of item by the number of items and then multiply by 23 (that is, the price of desired quantities required). We can also use this to find the number of pens required for Rs 800 similarly by using this formula.