**3. Mangala started doing physical exercise 10 minutes for the first day. She will increase the time of exercise by 5 minutes per day, till she reaches 45 minutes. How many days are required to reach 45 minutes?**

**Sol. Since the workout time Mangala increases by 5 minutes everyday after the first day, the successive workout times are in A.P.**

**Workout time for first day (a) = 10 minutes.**

**Increases in workout time (d) = 5 minutes**

**Let No. of days required to reach workout time of 45 minutes be ‘n’ days.**

**∴**

**tn = 45**

**tn = a + (n – 1) d**

**∴**

**45 = 10 + (n – 1) 5**

**∴**

**45 = 10 + 5n – 5**

**∴**

**45 = 5 + 5n**

**∴**

**45 – 5 = 5n**

**∴**

**5n = 40**

**∴**

**n =**

^{40}/_{5}**∴**

**n = 8**

**∴ 8 days required to reach work out time of 45 minutes.**