Question

A person on an exercise regime decides to lose $500$ calories in a day. For every $30$ minutes of exercise he loses $80$ calories but gains $25$ calories per cake that he eats. In the morning he exercises for a certain time and he eats a certain number of cakes. In the afternoon he exercise for double the time he eats thrice the number of cakes. In the evening he exercises for $1.5$ times the time he spends in the morning session and eats $4$ times the number of cakes he eats in the morning. Had he not eaten any cake he would have exceeded his target by $220$ calories. If he actually falls short of his target by $180$ calories then what is the number of cakes he has eaten in the evening?

• A. $12$
• B. $8$
• C. $16$
• D. $10$

Answer 1

The correct option is B $8$

Let the time for which he exercises in the morning be $x$ minutes and the number of cakes he eats in the morning be $y$.

So, total calorie gain $=\left(\frac{x}{30}\right)\times 8+25y-2\times \left(\frac{x}{30}\right)\times 80+75y-\frac{3}{2}\times \left(\frac{x}{30}\right)\times 80+100y$

Had he not eaten the cake, a calories loss is $12x=720\Rightarrow x=60$

In reality, he falls short by $180$ calories: $-720+200y=-320$

$\Rightarrow 200y=400$

$\Rightarrow y=2$

So, he eats $2\times 4=8$ cakes in the evening.