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A fruity tale

Fruits

Kharatmal is a fruit seller who sells fruits in our neighbourhood. One day Kharatmal had to go out of town with his family. But he did not wish to lose on business. Therefore, he asked Popatram, his domestic help, to sell the apples while he was away. Of course, Popatram would receive a commission.

But there was a problem! Popatram had never been to school and could not count beyond ten. Therefore, Kharatmal did not wish to burden Popatram with too much responsibility. He told Popatram to sell only the apples. People, usually, purchased fewer than ten apples and, so, Popatram's arithmetic would not be put to test.

Kharatmal departed for the town easy in mind, and Popatram left for the market with a basket of apples, that could hold at the most 600 apples, balanced on his head. Popatram carried another basket in which he kept a small rug, his turban, a snuff box, and such other things.

On reaching the market, Popatram placed the basket of apples in front, removed the rug from the other basket and sat on it after spreading it neatly. Customers were yet to arrive. In order to while away his time, Popatram began a game of his own. He removed two apples from the fruit basket at a time and transfered it to the other basket; thereafter he continued his experiment by removing three, four, five, six, seven, and eight apples at a time.

A customer arrived and to Popatram's grief, wanted to purchase the entire lot of apples. "How many apples are there?" he demanded to know.

Popatram was speechless for a moment, but he quickly recovered and said:

1. "If I keep transferring two apples at a time from the apples basket to the other basket, one apple remains in the apples basket."

2. "If I keep transferring three apples at a time from the apples basket to the other basket, two apples remain in the apples basket."

3. "If I keep transferring four apples at a time from the apples basket to the other basket, three apples remain in the apples basket."

4. "If I keep transferring five apples at a time from the apples basket to the other basket, four apples remain in the apples basket."

5. "If I keep transferring six apples at a time from the apples basket to the other basket, five apples remain in the apples basket."

6. "If I keep transferring seven apples at a time from the apples basket to the other basket, no apples remain in the apples basket."

7. "If I keep transferring eight apples at a time from the apples basket to the other basket, seven apples remain in the apples basket."

"Now, you figure out the number of apples from what I have told you because I cannot count," Popatram stated.

Since the basket wasn't very large, the customer decided to adopt the easier method: he counted the number of apples, paid Popatram the right amount, and left.

Unfortunately, we don't have the basket of apples before us. We will have to calculate the number of apples from Popatram's clues. Can you tell how many apples were there in the basket?






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  • 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