# Borrowing a Bike Is No Fun!

It was lunch break at the office. My home is quite close to the office, so I go home for lunch.

I went to the parking lot and, to my dismay, found that my bike had a flat. I had no time to fix the flat now; I could do it after the office closed for the day.

I rushed to the office cafeteria where Shaswat was having lunch. I told him about my troubles and requested him to lend me his bike. The guy gave me the key to his bike unwillingly.

"What is the registration number of your bike?" I knew the model, but you always find many bikes of the same model in the parking lot and they all look the same. I did not want to get beaten for picking up the wrong bike.

"The registration number of my motorcycle is a four-digit number. The first three digits of the number are in an arithmetic sequence, and the last three digits are in a geometric progression. The last digit is four times the first digit plus one. Figure out the number and go home and have lunch."

I get only a 30-minute lunch break, and I had already lost several valuable minutes going to the parking lot, rushing to the cafeteria, and listening to Shaswat's drivel. I pleaded with him to tell me the number, and he did. But can you figure out the number? I will repeat the essential details:

1. The bike's number is of four digits.

2. The first three digits of the number are in arithmetic progression, and the last three digits are in geometric progression.

3. The last digit is four times the first digit plus one.

• 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