July 2011

# Solution

Pramod is 28 years old and his father is 58.

Let Pramod's age be y and that of his father be x. Then, x - y = 30 and xy = 1624.

Therefore, (x-y)2 = 900. That is, x2 - 2xy + y2 = 900.

Now, x2 - 2xy + y2 = 900 can be re-written as: x2 + 2xy + y2 - 4xy = 900.

But, x2 + 2xy + y2 = (x + y)2.

Therefore, (x + y)2 - 4xy = 900.

We have xy = 1624. So, 4xy = 4 x 1624 = 6496.

Therefore, (x + y)2 - 6496 = 900. So, (x + y)2 = 7396.

Therefore (x + y) = square-root (7396). Therefore, x + y = + or - 86. But we are considering ages and, so, x + y cannot be negative. So, (x + y) = 86.

Now, (x + y) = 86 and (x - y) = 30. Adding the two: 2x = 116; therefore x = 58. x - y = 30; so, 58 - y = 30. Therefore, y = 28.

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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