A Problem of Shopping

                        Meena went out for shopping. She had in her handbag approximately Rs. 15/- in one rupee notes and 20 p. coins. When she returned she had as many one rupee notes as she originally had and as many 20p. Coins as she originally had one rupee notes. She actually came back with about one- third of what she had started out with.

              How much did she spend and exactly how much did she have with her when she started out?

 

 Answer:     Let us assume that originally Meena had X rupees and Y 20 paise coins. Going shopping she had (100 X + 20 Y) paise

She returned with only (100 y +20 x) paise.

This last sum, as we know, is one –third of the original and therefore

3(100 Y +20 X) = 100X + 20 Y

Simplifying we have X= 7 Y

If Y is 1 then X is 7. Assuming this so Meena had 7.20 rupees when she set out for shopping.

This is wrong because Meena actually had about 15 rupees.

Let us see now what we get if Y= 2. Then X= 14.

 The original sum was 14.40 rupees which accords with the condition of the problem.

If we assume that Y= 3 then the sum will be too big - 21.6 rupees.

Therefore the only suitable answer is 14.40 rupees.

 After shopping Meena had 2 one rupee notes and 14 twenty Paise coins.

This is actually 1/3^rd of the original sum 1.440: = 480.

Meena’s purchases, therefore, cost 14.40 – 4.80 = Rs. 9.60