Question

Anil and anshu arrived late in the party.they found that only 5/6of the cake was left .anil ate 1/5 of it and the rest was eaten by anshu . What fraction of the cake did anshu eat?

Answer 1

Step-by-step explanation:

total left cake is 5/6

anil ate 1/5/5/6

then anshu ate 5/6-1/5/5/6

so anshu ate 89/159

Answer 2

The fraction of cake ate by anshu is 2/3rd of the cake

Solution:

Given, Anil and anshu arrived late in the party.

They found that only 5/6 of the cake was left  

Anil ate 1/5 of it and the rest was eaten by anshu  

We have to find what fraction of the cake did anshu eat?

Now, according to given information,  

fraction of cake eaten by anshu = left part of cake – part eaten by anil

= 5/6 of cake  - anil ate 1/5 of left cake

= 5/6 of cake – 1/5 of (5/6 of cake)

$=\frac{5}{6} \text { of cake }-\frac{1}{5} \times \frac{5}{6} \text { of cake }$

$=\left(\frac{5}{6}-\frac{1 \times 5}{5 \times 6}\right) \text { of cake }$

$\begin{array}{l}{=\left(\frac{5}{6}-\frac{1}{6}\right) \text { of cake }} \\\\ {=\left(\frac{5-1}{6}\right) \text { of cake }}\end{array}$

$=\frac{4}{6} \text { of cake }=\frac{2}{3} \text { of cake }$

Hence, anshu ate 2/3rd of the cake.