Financial details of the deals were however not disclosed.
The stock soared 6 per cent to end at Rs 632.70 on BSE. During the day, it surged 12.7 per cent to Rs 672.75.
At NSE, shares of the company zoomed 6 per cent to close at Rs 630.55.
On the volume front, 3.73 lakh shares were traded on BSE and over 19 lakh shares changed hands at NSE during the day.
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The deal would also give a boost to Quess' operations in Asia Pacific markets as Malaysia, the Philippines and Sri Lanka, where it operates, it added.
Initially, the Quess will acquire 64 per cent stake in Comtel, while the balance would be acquired in a phased manner over 2018-20, it added.
The Bengaluru-based company will also acquire 49 per cent stake in Terrier Security Services India Pvt Ltd, marking its entry into the manned guarding and security solutions business, Quess Corp said in another filing to BSE.