Latest M4maths Aptitude Question SOLUTION: A pencil cost rs. 0.25 ,a pen cost rs. 10 and a book cost rs. 25 .How many each,one should buy so that the total no. of article is 100 and the total amount is rs. 1000?

There are three solutions.

Number of pencils = C Number of books = B Number of Pens = P

Total Number of articles = 100 = C + P + B
C = 100 – P - B -- equation 1

Total Purchase:

0.25 * C + 10 P + 25 * B = 1,000 , multiply by 4
C + 40 P + 100 B = 4,000 --- equation 2

From the above equations, we can infer that maximum value of P is 100, maximum value of B is 40 and Maximum value of C is 100. Minimum of any of them is 1. If the values are more than those maximum then equation 1 or 2 will not be satisfied.

As C + 40 P + 100 B = 4,000 , substitute value of C from equation 1
100 - P - B + 40 P + 100 B = 4,000
39 P + 99 B = 3900 divide by 39

P + (33/13) B = 100 -- equation 3

Here, 100 is an integer. P is an integer. So (33 B/13) is also an integer.
So B = 13, 26, or 39 only three possibilities.

1) B = 13, P + 33 = 100, P = 67
C = 100 - 13 - 67 = 20.
Total purchase = 20*0.25 +10*67 + 13*25 = Rs 1,000

2) B = 26, P + 33 * 26/13 = P + 66 = 100, P = 34
C = 100 - 26 - 34 = 40
Total purchase = 40*0.25+10*34+25*26 = Rs 1,000

3) B = 39 , P + 99 = 100, P = 1
C = 100 - 39 - 1 = 60
total purchase = 60*0.25 + 1 * 10 + 39 * 25 = Rs 1,000