Question

Shyam visited Ram during his brief vacation. In the mornings they both would go for yoga. In the evenings they would play tennis. To have more fun, they indulged only on 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, $14$ evening when they stayed at home and total of $22$ days when they did yoga or played tennis. For how many days Shaym stayed with Ram?

• A. $20$
• B. $25$
• C. $30$
• D. $40$

Answer 1

The correct option is C $30$

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

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

Given that $24$ mornings they did nothing. So those days, either they played tennis in the evening or stayed at home all day.

Hence $y+z=24$ ---(1)

$14$ evenings they stayed at home. So they either did yoga in morning or stayed home all day

$x+z=14$.----(2)

Now $22$ days they did yoga or played tennis.

$x+y=22$ ---(3)

From (1), $z=24-y$

Substituting in (2)

$x+24-y=14⟹x-y=-10$ ---(4)

(3)+(4)$⟹2x=12\therefore x=6$

$\therefore y=22-x=16$

and $z=24-y=8$

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