GAP-W International, L.P.

Exhibit 10.2

EXECUTION VERSION

Letter Agreement

Amendment No 1.

October 25, 2012

Genpact Limited

Canon’s Court

22 Victoria Street, Hamilton HM

Bermuda

Ladies and Gentlemen:

Reference is made to that certain letter agreement, dated August 1, 2012 between Genpact Limited, an exempted limited company organized under the laws of Bermuda (the “Company”) and each of the undersigned shareholders of the Company (the “Letter Agreement”). All capitalized terms used herein shall, unless otherwise provided herein, have the meanings ascribed to such terms as set forth in the Letter Agreement. The parties hereto hereby agree as follows:

Existing Investors), Article IV of the Existing Shareholders Agreement and all rights and obligations of the Company and the Existing Investors associated therewith (and any definitions or provisions thereunder necessary to carry out the terms of such Article) shall remain in full force and effect for 90 days after the closing of the Share Purchase and shall thereafter terminate notwithstanding anything herein or in the Existing Shareholders Agreement to the contrary. Following reasonable notice from the Existing Investors, the Company agrees to assist the Existing Investors with such block trades, broker-dealer transactions or ordinary brokerage transactions by causing its officers and employees to participate in customary confirmatory due diligence sessions (for transactions of the type contemplated hereby) with prospective purchasers of the Existing Investors’ Company Common Shares, except that, for the avoidance of doubt and notwithstanding anything in the Existing Shareholders Agreement to the contrary, the Company shall not be required to participate in any “road show” or other in-person meetings with prospective purchasers, and any such sessions shall be subject to the availability of the Company’s officers and employees and scheduled so as to minimize disruption to the Company’s business.

Notwithstanding anything herein or in the Existing Shareholders Agreement to the contrary, the Existing Investors shall be responsible for all reasonable expenses of the Company (including filing fees, expenses of counsel and independent accountants and all other “Registration Expenses” as defined in the Existing Shareholders Agreement), in addition to their own expenses, in respect of any block trades, broker-dealer transactions or ordinary brokerage transactions effected pursuant to Article IV of the Existing Shareholders Agreement.

Notwithstanding anything herein or in the Existing Shareholders Agreement to the contrary, the Existing Investors agree that the Company shall have no obligation to register Company Common Shares or effect a Shelf Take-Down (as defined in the Existing Shareholders Agreement) on behalf of the Existing Investors pursuant to Article IV of the Existing Shareholders Agreement (i) before the filing of the Company’s Form 10-Q for the Quarter Ended September 30, 2012, (ii) after December 15, 2012 or (iii) at any time the Company determines that a Valid Business Reason (as defined in the Existing Shareholders Agreement) exists.

Notwithstanding anything herein and in the Existing Shareholders Agreement to the contrary, the Existing Investors agree that, following the closing of the Share Purchase, (i) the OH Investors (taken together) on the one hand and the GA Investors (taken together) on the other hand shall each be limited to one (1) Shelf Take-Down pursuant to Article IV of the Existing Shareholders Agreement; provided, that the OH Investors may participate in a Shelf Take-Down by the GA Investors and the GA

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Investors may participate in a Shelf Take-Down by the OH Investors (in each case with the other party’s consent), and in each case such joint Shelf Take-Down shall be treated as only one (1) Shelf Take-Down for purposes of this Letter Agreement and (ii) the OH Investors (collectively) and the GA Investors (collectively) each may not transfer pursuant to all Shelf Take-Downs effected pursuant to Article IV of the Existing Shareholders Agreement more than half of the number of Company Common Shares held by the OH Investors (collectively) and the GA Investors (collectively), respectively, immediately after the Share Purchase, which amount may be upsized by an additional 20% of such number of Company Common Shares with the prior consent of the Company (which consent shall not to be unreasonably withheld or delayed). The GA Investors and the OH Investors shall communicate with each other in good faith to determine an appropriate offering size for any joint Shelf Take-Downs.”

[Remainder of page intentionally blank; signature pages follow]

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IN WITNESS WHEREOF, the undersigned have duly executed this letter agreement, all as of the date first written above.

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