# 57 Times Smaller Number

It was Sunday. Ma wanted me to get her some vegetables from the market, about one kilometre from home.

Shashi is my next-door neighbour. I went to his house, hoping he would give me company.

I found Shashi scribbling away furiously. There were papers strewn on the floor. He was so busy that he did not even notice me.

"Hey, what are you doing?" I asked.

Shashi gave a start of surprise at my sudden intrusion.

"Can't you see?" he retorted, sounding annoyed.

Now, Shashi is a person who hardly ever gets annoyed. If he was annoyed, it meant something was certainly troubling him.

"What's bothering you?" I asked. "Tell me; I could help."

"You! Brother, you get heart palpitations at the mention of the word, maths. I am trying to solve a maths problem."

He was right. Maths and I don't get along well.

"What is the problem you are trying to solve? If you discuss the problem with me, you might feel better," I suggested.

"Okay. I am trying to find a positive integer number — it could have any number of digits — that becomes 57 times smaller when the first digit (leftmost digit) is deleted."

I could make nothing of what he said. "Please explain," I said.

"Okay, blockhead. I am trying to find a positive integer, say, xyzwrst. It can have any number of digits. When I delete "x", the first digit (the leftmost digit), I get yzwrst, which is also a positive integer. Now, yzwrst should be 57 times smaller than the original number, xyzwrst. In other words, xyzwrst should be equal to yzwrst × 57. Got it?"

Of course, I didn't get it.

"I can help you find the solution," I said.

"You!" Shashi was dumbfounded.

"Yes, I can. Come along with me to the market; the fresh air outside will stimulate your brain, and you will think up a way to solve the problem at once."

The idea appealed to Shashi; he agreed to come along with me.

By the time we return from the market, please solve this problem. I wish to see Shashi in his pleasant mood.

Some useful links for

• 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