Question

man is eating a cheese pizza and he is fond of it. During the first day he eats the half of the pizza. On the second day, he eats the 1/3rd of the remaining part of the pizza. The third day he eats 1/4th of what is left and 4th day he eats 1/5th of what still remains. He continues eating pizza in the same process of fraction like on 5th day he eats 1/6th, on 6th day he eats 1/7th of what remains and so on.

i) If pizza got stale after 4th day when fraction of original pizza is still available? *

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Answer 1

Step-by-step explanation:

Let us assume that the total pizza is 1.

During the first day the man eats the half of the pizza, meaning,

1×12

.

So the remaining pizza after first day is

(1−12)⇒12

We can represent the pizza eaten by this diagram.

On the second day, the man eats 13rd

of the remaining part of the pizza, meaning,

12×13⇒16

We will get the remaining pizza after second day as,

(12−16)

We know the LCM of 2 and 3 is 6. Now,

⇒3−26⇒26⇒13

The third day the man eats 14th

of what is left, meaning,

13×14⇒112

After subtracting 112

from 13

we will get the remaining pizza after second day as,

(13−112)

We know the LCM of 3 and 12 is 12. Now,

⇒4−112⇒312⇒14

Similarly on the fourth day the man eats 15th

of what still remains.

14×15⇒120

After eating 15th

Part of pizza remaining pizza after fourth day will be,

(14−120)

We know the LCM of 4 and 20 is 20. Now,

⇒5−120⇒420⇒15

He stopped eating after that because the last piece was not fresh.

15th

fraction of the original pizza is still available.