What's the limit duration that clients must answer to a variation order sent by main Contractor ?

If you are asking where the Client's should be response the proposed variation or notification leading for variation submitted by the Contractor, the Contract Document definitely the number of days is mentioned in the Standard Condition of Contract. if in case have not found or not stated in the Contract Document please check in what type of Contract to be used, e.g. FIDIC.

Limitless since these works would not start until he/she accepts.

Any variation to the original Scope of Work is called Variation Order.  It could have positive or negative time or cost impact.  In very rare cases it might have neither cost nor time impacts.In some cases it is not easy to determine whether an order from the owner (or client) is a variation to the original Scope of Work or a part of the original Work which is stated in the contract and its attachments or specifications.)  As soon as both parties (contractor and owner) agree that an order is a variation to the originally mutually agreed scope of work, they need to find a way to calculate or estimate its cost and time impacts.  The method to calculate or estimate cost and time impacts are normally mentioned in the contract.It might be necessarily essential to mention that even changing the specifications, execution methods could be considered as variation order.  Many construction specialists say as a rule of thumb anything beyond the contractor's control which might affect cost and time delivery targets could be a variation order.  To me it is not true and might mislead everyone.

A variation order is issued whenever there is a variation to the contracted works. This may include adding or omitting work, increasing or decreasing the quantity of any work, changing the character or quality of any material or work, the order in which the works proceed etc.How and who values variation orders should be included in the contract documents. Not all variation orders require a variation in the contract cost e.g. substitution of similar materials or a change in the colour of a material. Variations can be requested by either the Contractor or Principal or come about as a result of conditions outside the control of either party e.g. bad weather.In construction projects the most disputed variation orders are extensions of time, particularly where concurrent delays (a delay caused by the Contractor and a delay caused by the Principal both negatively affecting the critical path occur simultaneously) are concerned as these often have significant cost attached.