A Cycling Trip: Solution

When we don't know something, our old friends x and y come to the rescue.

We don't know how many bicycles and tricycles were there in the shop. Let there be "x" bicycles and "y" tricycles.

A bicycle has two wheels, so "x" bicycles have 2x wheels. A tricycle has three wheels, so "y" tricycles have 3y wheels. The total number of wheels is 132. Therefore, 2x + 3y = 132. Let me call this Equation I.

A bicycle has two pedals, so "x" bicycles have 2x pedals. A tricycle also has two pedals, so "y" tricycles have 2y pedals. The total number of pedals is 112. Therefore, 2x + 2y = 112. Let me call this Equation II.

Subtracting Equation II from Equation I, we get (2x + 3y) - (2x + 2y) = 132 - 112.

So, 2x + 3y - 2x - 2y = 20.

So, y = 20.

Thus, there were 20 tricycles in the shop.

I can substitute the value of "y" in any of the equations to get the value of "x". I choose Equation II. 2x + 2y = 112. So, 2x + 2(20) = 112. Therefore, 2x + 40 = 112. So, 2x = 72. Thus, x = 36. There were 36 bicycles in the shop.

Some useful links for
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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 Communication - 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