October 2015

Find their ages

Geometrical figures

I went to pick up my son from school. The school bell rang and all the children poured out of their classrooms and were out of school in a flash.

As I waited for my son I saw five boys assemble in the playground and stand in a neat row. A teacher came up. I felt sorry for the boys; perhaps they had played some mischief and had been asked to stay back as punishment, I thought. I shouldn't have interfered but curiosity got the better of me and I asked the teacher why were the boys being punished.

"Punished!" he was taken aback. "They are not being punished," he informed. "They are from different grades and have been selected to perform at a school function," he said. The five boys had assembled to rehearse.

"oh!" I said quite relieved.I should have gone away then and left the boys and the teacher to their practice. But, no! I remembered my own school days when teachers tortured me by asking questions. I wanted to take revenge by reversing roles and asking questions now. "How old are they?" I asked.

The teacher looked at me scornfully; he was getting late. But he answered nevertheless: "The boys, as you can see, are standing in a single row. They are standing in the ascending order of their ages from left to right. The left-most or the youngest boy is 6 years old, the boy next to him is 9 years old and the right-most boy, who is the oldest among them, is 13. The age of the boy in the middle is equal to the average age of all the five boys. No two boys are of the same age. Now I leave it to you to find out the ages of the other two boys.

My head swam. I realized I should not have annoyed a teacher.

"Oh, by the way it is a coincidence that both the boys, whose ages you have decided to calculate, celebrated their birthdays today," the teacher informed and handed me two pieces of cake. "Shall I give a paper to do your calculations?" he asked. "No," I murmured, "I will solve the problem at home." I did not stay there a minute longer. Will you please help me find the ages of the two boys?

Click here for the solution

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

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