57 Times Smaller Number

Wastepapers strewn on the floor

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.

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  • Union Public Service Commission - www.upsc.gov.in
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  • Indian Statistical Institute - www.isical.ac.in
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  • Indian Institute of Management, Ahmedabad - www.iimahd.ernet.in
  • Indian Institute of Mass Commission - www.iimc.nic.in
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  • 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