Shiv visited Ramesh on vacation. In the morning, they both would go for yoga. In the evenings, they would play tennis. To have more fun, they indulge only in one activity per day,i.e., either they went for yoga or played tennis each day. There were days when they were lazy and stayed home all day long. There were 24 mornings when they did nothing, 14 evenings when they stayed at home, and a total of 22 days when they did yoga or played tennis. For how many days Shiv stayed with Ramesh?

Let the number of days they did yoga be x and the number of days they played tennis be y.

The number of days when they stayed home all day was z.

Given that 24 mornings, they did nothing.

In those days, they either played evening tennis or stayed home all day.Hence y+z=24 ---(1)

Fourteen evenings, they stayed at home. So they either did yoga in the morning or stayed home all day x+z=14.----(2)

Now, 22 days, they do yoga or play tennis.x+y=22 ---(3)

From (1), z=24−y

Substituting in (2) x+24−y=14
x−y=−10 ---(4)

(3)+(4) 2x=12 giving x=6y=22−x=16

and z=24−y=8

Hence, the total number of days = x+y+z=6+16+8=30