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# Pen & Note Books Problem | PRMO-2019 | Question 16

Try this beautiful Problem from Algebra based on Pen & Note Books from PRMO 2019, Question 16. You may use sequential hints to solve the problem.

Try this beautiful Problem from Algebra based on Pen & Note Books from PRMO 2019.

## Pen & Note Books – PRMO 2019, Problem 16

A pen costs Rs.13 and a notebook costs Rs.17. A school spends exactly Rs.10000 in the year 2017 – 18 to buy x pens and y notebooks such that $x$ and $y$ are as close as possible (i.e. $|x-y|$ is minimum). Next year, in $2018-19,$ the school spends a little more than Rs.10000 and buys y pens and x notebooks. How much more did the school pay?

• $9$
• $40$
• $34$

### Key Concepts

Algebra

Equation

multiplication

Answer:$40$

PRMO-2019, Problem 16

Pre College Mathematics

## Try with Hints

Given A pen costs Rs.$13$ and a note book costs Rs.$17$

Nunber of pens $x$ and numbers of notebooks $y$

According to question

$13 x+17 y=10,000$ ……………………..(1)
$17 x+13 y=10000+P$………………….(2)

Where $\mathrm{P}$ is little more amount spend by school in $2018-19$.we have to find out the value of $P$.Can you find out?

Can you now finish the problem ……….

$x+y=\frac{20,000+P}{30}$

Subtract (1) form (2)

$x-y=\frac{P}{4}$

Let $P=4 a$
\begin{aligned} \text { So, } x+y=& \frac{20,000+4 a}{30} \ &=666+\frac{10+2 a}{15} \end{aligned}

Therefore $a$=$10$

Can you finish the problem……..

Since $P=4 a$ $\Rightarrow P=40$

So school had to pay Rs. 40 extra in 2018 – 2019