Enjoy the Flight!

My uncle, who loves to put me in a tight corner by asking me maths puzzles, arrived on his annual visit to us. This time, he came by air. Imagine that! I have never been anywhere near an aircraft, leave alone travelling on one.

I have only seen planes flying high up in the air, and they look tiny from below. They can't be carrying many passengers.

"Uncle," I said, "planes are so small. They can't be carrying many passengers, can they?"

I should not have opened my mouth. "Airplanes can be huge and can carry a large number of people. Do you know how many people were there on the plane with me?" my uncle asked.

Of course, I did not know. I said so.

Well, there were 20 rows of seats in the plane. All the rows had the same number of seats. The total number of seats in each row was the greatest number that divides 34, 43, 70, 124, and 358 and leaves the same remainder in each case. Now, tell me how many passengers were there on the plane.

I had asked for it! I should not have opened my mouth. Can you help me find the total number of passengers on the plane?

• 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