I am an Indian citizen. I have lost my passport in India and I have applied for a new passport and got it. My Singapore visa mentioned the old passport number. Is there any problem with traveling to Singapore?
Odds are no, you cannot, because the airline will most likely refuse to let you board your flight if you cannot show them the visa.
Usually you could visit Singapore simply by bringing both your old and new passport, but in this case you've actually lost your passport. I would advise getting in touch with the nearest Singapore embassy/high commission/consulate and asking if it's possible to transfer the visa to a new passport:
Q: How do I transfer my valid visa from my old passport to the new one?
A: For transfer of visa, please submit your old and new passport (original and copy), the valid visa, and the fulfilled Form 14 and your 2 inches colored photos to the Consulate-General between Monday to Friday 9:00am – 11:00am.
Singapore will have electronic records of your old visa, but you will probably need a photocopy showing the passport number and a police report certifying the loss and cancellation of the old passport.
You should wait till you have your new passport. You can not travel without a passport. Your old visa will be verified under your old PPN. Just bring along a copy of old passport number or a copy of your passport application. Usually all they need is the number and date of birth. The name must have not changed. You can get a 3-day business visa issued at the airport before you board your plane so when you arrive you will need to make an appointment with immigration for a long term stay. Why you did not Photostat your old passport? Shame on you. Most embassy require that you leave a photo ID at the gate with the guard and business card when you enter compound. A color photocopy PPN works great for this.