Method of praying Qaza Salahs quickly
 

If someone have missed Salahs in their account. Either one time's or of many years, they must pray their Qaza as soon as possible. Salah is a Fard and not forgiven. On the day of judgement Salah will be the first thing asked about.
For the people who have many years of missed Salahs. There is a way to pray them quickly. Following instructions have four exeptions and has all Fards and Wajibs for a complete Salat. Please pray your Qaza as soon as possible. Even of you could pray one days Qaza Salahs every day which are only 20 rakahs (3 wajib witr), please do it. It only takes few mins to perform 20 rakahs according to the following instructions.

1) In Ruku and Sajdah instead of reciting "Subhaana Rabbiyal Azeem" and "Subhaana Rabbiyal A'la" three times, say it only once. But make sure do not leave Ruku poster untill the Meem (M) of Azeem has been said properly. Similarly do not leave the posture of Sajdah until Ala has been said completely. Just make sure to say these Tasbeehaat properly and do not rush.

2) In third and four Rakah of Fard Salah instead of reciting the whole Soorah Fatiha say, "Subhan Allah" three times and go to Ruku, . Make sure "Subhan Allah" has been recited three times properly, do not rush. This exeption is only for Fard. In third rakah of Witr it's a must to recite full Soorah Fatiha followed by at least three ayahs of Quran or a soorah (as we usually do in first and second rakah).

3) In last Qaidah (when we sit for Attahyyat) before Salam, after Attahyyat instead of full Durood and Dua just say, "Allah Humma Salle Ala Sayedena Mohammad Wa Aalihi", then finish the Salat with Salam. Dua is not a must here.

4) In Witr, instead of full Dua-eQunoot just say "Rabbigh Fir Lee" one or three times.

(Fatawa Rizvia, Part 3, Page 622)