﻿ Youthaffairz | Teaser: Festival shopping
November 2015

# Solution

Let's suppose I started off with "x" rupees in my pocket.

I visit the first shop and spend 100 rupees more that half of "x"; this means I spend (x/2 + 100) rupees in the first shop. So, I am left with x - (x/2 + 100); thus, I am left with (x - 200)/2.

In the second shop I spend 100 rupees more than half of what I have left. So, I spend [(x - 200)/4 + 100]. On coming out of the second shop I am left with (x - 200)/2 - [(x - 200)/4 + 100]. Thus, I am left with (x - 600)/4.

In the third shop I again spend 100 rupees more than half of what I have left; so, I spend [(x - 600)/8 + 100]. On coming out of the third shop I am left with [(x - 600)/4] - [(x - 600)/8 + 100]. So, I am left with (x - 1400)/8.

In the fourth shop I spend 100 rupees more than half of what I have left; so, I spend [(x - 1400)/16 + 100]. On coming out of the fourth shop I am left with (x - 1400)/8 - [(x - 1400)/16 + 100]. So, I am left with (x - 3000)/16.

In the fifth shop I spend 100 rupees more than half of what I have left; so, I spend [(x - 3000)/32 + 100]. On coming out of the fourth shop I am left with (x - 3000)/16 - [(x - 3000)/32 + 100]. So, I am left with (x - 6200)/32.

But on coming out of the fifth shop I am left with no money. So, (x - 6200)/32 = 0. Thus, x - 6200 = 0. So, x = 6200. I, therefore, started with Rs 6200 in my pocket.

Let's work backwards to see if I got the answer right. I have 6200 rupees and enter the first shop. I spend (6200/2 + 100). Thus, I spend 3200. I am left with 3000.

In the second shop I spend 3000/2 + 100 = 1600. I am left with 1400.

In the third shop I spend 1400/2 + 100 = 800. I am left with 600.

In the fourth shop I spend 600/2 + 100 = 400. I am left with 200.

In the fifth shop I spend 200/2 + 100 = 200. I am left with no money.

Some useful links for
your career:

• Union Public Service Commission - www.upsc.gov.in
• IIT-Kharagpur - www.iitkgp.ac.in
• Indian Statistical Institute - www.isical.ac.in
• Indian Institute of Technology Madras - www.iitm.ac.in
• Indian Institute of Management, Ahmedabad - www.iimahd.ernet.in
• Indian Institute of Mass Commission - www.iimc.nic.in
• IIT Bombay - www.iitb.ac.in
• Indian School of Mines, Dhanbad - www.ismdhanbad.ac.in
• Birla Institute of Technology, Ranchi - www.bitmesra.ac.in
• Central Institute of Fisheries Nautical and Engineering Training - www.cifnet.nic.in
• Indian Institute of Information Technology, Allahabad (Deemed University) - www.iiita.ac.in
• Central Marine Fisheries Research Institute, Kochi - www.cmfri.com
• Tata Institute of Social Sciences, Mumbai - www.tiss.edu

DISCLAIMER: The contents of this website are for informational purposes only. Although due care is taken, the correctness and accuracy cannot be guaranteed. The science and medical research articles are for informational purposes only, aimed at kindling an interest in science. They are not intended to provide any kind of advice.