Ashok purchased pens and pencils in the ratio $2:3$ during his first visit and paid Rs. 86 to the shopkeeper. During his second visit, he purchased pens and pencils in the ratio $4:1$ and paid Rs. 112. The cost of a pen as well as a pencil in rupees is a positive integer. If Ashok purchased four pens during his second visit, then the amount he paid in rupees for the pens during the second visit is __________.

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Alternate Method

Let's denote the cost of one pen as $₹ x$ and one pencil as $₹ y$.

In the first visit, Ashok bought pens and pencils in ratio $2: 3$.

If he bought $2 k$ pens and $3 k$ pencils, then:

Total cost $=2 k x+3 k y=86$

In the second visit, Ashok bought pens and pencils in ratio $4: 1$.

We're told he bought $4$ pens, so he must have bought $1$ pencil.

Total cost $=4 x+y=112$

From the equations:

$\begin{aligned} & 2 k x+3 k y=86 \ldots \\ & 4 x+y=112 \ldots \text { (2) } \end{aligned}$

From equation (2): $y=112-4 x$

Substituting into equation (1):

$\begin{aligned} & 2 k x+3 k(112-4 x)=86 \\ & 2 k x+336 k-12 k x=86 \\ & -10 k x+336 k=86 \\ & x=\frac{336 k-86}{10 k} \end{aligned}$

For $x$ to be a positive integer, $(336 k-86)$ must be divisible by $10 k$.

Trying $k=1: x=\frac{336-86}{10}=\frac{250}{10}=25$

This gives $y=112-4(25)=112-100=12$

Verifying our answer:

First visit: $2(1)(25)+3(1)(12)=50+36=86 \checkmark$

Second visit: $4(25)+1(12)=100+12=112 \checkmark$

Therefore, during the second visit, Ashok paid $4 \times ₹ 25=₹ 100$ for the pens.