A pencil costs Rs. 0.25, a pen costs Rs. 10 and a book costs Rs. 25. How many each, one should buy so that the total number of articles is 100 andthe total purchase is Rs. 1000?

1
by yatiyamini

2014-10-11T00:41:21+05:30

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
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