IPMAT Indore 2020 (SA) - 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 __________. | PYQs + Solutions

IPMAT Indore 2020

Arithmetic

Ratio, Proportion & Variation

Easy

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 __________.

Entered answer:

✅ Correct Answer: 100

\newline

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:

\newline

\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):

\newline

\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.