Question

. Shivam and Varun ate 95 toffees altogether. Varun
and Aakash ate 216 toffees altogether. If Varun ate1/5
of what Aakash ate, then how many toffees did
Shivam eat?
A. 59
B. 65
C. 70
D 79​

Answer 1

$\fontsize{18}{10}{\textup{\textbf{The correct option is (A) 59.}}}$

Step-by-step explanation:  

Let x, y and z represents the number of toffees ate by Shivam, Varun and Akash respectively.

Then, according to the given information, we have

$x+y=95~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y+z=216~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\y=\dfrac{1}{5}z\\\\\Rightarrow z=5y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Substituting the value of z from equation (iii) in equation (ii), we get

$y+5y=216\\\\\Rightarrow 6y=216\\\\\Rightarrow y=36.$

From equation (i), we get

$x+36=95\\\\\Rightarrow x=59.$

Thus, the required number of toffees that Shivam ate is 59.

Option (A) is CORRECT.

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