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 (1/3)rd of the remaining part of the pizza. The third day he eats (1/4)th of what is left and 4th day he eats (1/5)th of what still remains. He continues eating pizza in the same process of fraction like on 5th day he eats (1/6)th, on 6th day he eats (1/7)th of what remains and so on. What fraction of pizza he would eat on 7th day if pizza is still fresh.​

Answer 1

Answer:

He will be eating 1/8 of the pizza which is 7/56 = 1/8

Step-by-step explanation:

Day 1 . He eats 1/2 pizza.

=> Remaining = 1/1 - 1/2

                       = 2/2 - 1/2

                       = 1/2

Day 2 . He eats 1/3 of the remaining.

=> Remaining = 1/2 * 1/3

                       = 1/6

                       =1/2 - 1/6

                       =3/6 - 1/6

                       =2/6

                       =1/3

Day 3 . He eats 1/4 of the remaining.

=> Remaining = 2/6 * 1/4

                       = 2/24

                       =1/12

                       =2/6 - 1/12

                       =4/12 - 1/12

                       =3/12

                       =1/4

Day 4. He eats 1/5 of the remaining.

=> Remaining = 1/4 * 1/5

                       = 1/20

                       =3/12 - 1/20

                       =15/60 - 3/60

                       =12/60

                       =1/5

Day 5. He eats 1/6 of the remaining.

=> Remaining = 1/5 * 1/6

                       = 1/30

                       =1/5 - 1/30                      

                       =6/30 - 1/30

                       =5/30

                       =1/6

Day 6. He eats 1/7 of the remaining.

=> Remaining = 1/6 * 1/7

                       = 1/42

                       =1/6 - 1/42

                       =7/42 - 1/42

                       =6/42

                       =1/7

Day 7. He eats 1/8 of the remaining.

=> Remaining = 1/7 * 1/8

                       = 1/56

                       =1/7 - 1/56

                       =8/56 - 1/56

                       =7/56

                       =1/8

I hope it is correct.

Answer 2

Answer:

He would eat on 7th day $\frac{1}{112}$part of remaining pizza.

Step-by-step explanation:

1st day,

The man eats $\frac{1}{2}$of pizza.

So, remaining pizza=$1 - \frac{1}{2} = \frac{1}{2}$

2nd day,

He eats $\frac{1}{3}$rd of the remaining pizza.

So,left part of pizza $= \frac{1}{2} - \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$

3rd day,

The man eats $\frac{1}{4}$part of remaining.

So remaining $= \frac{1}{6} - \frac{1}{6} \times \frac{1}{4} = \frac{1}{8}$

4th day,

He eats$\frac{1}{5}$Of left part.

So now left part of pizza $= \frac{1}{8} - \frac{1}{8} \times \frac{1}{5} = \frac{1}{10}$

5th day,

He eats $\frac{1}{6}$of remaining part.

Now left part of pizza $= \frac{1}{10} - \frac{1}{10} \times \frac{1}{6} = \frac{1}{12}$

6th day,

The man eats $\frac{1}{7}$of left part.

Now left part of pizza$= \frac{1}{12} - \frac{1}{12} \times \frac{1}{7} = \frac{1}{14}$

By this sequence on the 7 th day the man would eat $\frac{1}{8}$part of remaining $\frac{1}{14}$part of pizza.

i.e$\frac{1}{14} \times \frac{1}{8} = \frac{1}{112}$