# Become Normal!!

Robi is a very serious student.

On the first day of this year his seriousness for study was 1 hour.

But after that day he increases his seriousness for study everyday by 10 minutes!!

On the other hand Fariha is a very crazy girl!!

On the first day she showed her craziness to her parents for 2 hours!!

And everyday she decreases her craziness for 2 minutes.

Now can we find out on which date both Robi and Fariha will become normal again?

**Notes:**

1.His/her seriousness or craziness can’t be negative or more than 24 hours.

2.After the day, he/she become normal, he/she again starts to increase his/her seriousness/craziness.

3.Look on the first day Robi was normal but not Fariha.

4.When he/she reaches the limits he/she, all on a sudden, becomes normal.

Both are in Arithmetic Progression then

in Robi’s case

a=1

d=10/60=1/6

tn=24

a+(n-1)d=tn

1+(n-1)1/6=24

(n-1)1/6=23

(n-1)=138

n=139

**So in 139 days Robi’s seriousness reach 24 hours then we can assume in 140 day his Seriousness become normal**

In Fariha’s case a=2

d=2/120=1/60

tn=0

here n=121

**So in 121 days Fariha’s craziness becomes normal.**

so both will become normal again lcm(121,140)=16940.

Answer is* 16940 *[Assuming Robi ‘s seriousness can reach 24 hours and next day it become normal, if in the same day of reaching 24 hours his seriousness becomes normal then answer will be (121,139)=16819 ]

### Your Answer

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