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Olympiad workbook
Exam
Olympiad workbook
Subject
IOQM
Chapter
Basics of Mathematics

Olympiad workbook · IOQM · Basics of Mathematics

A pen costs Rs. 13 and a note book costs Rs. 17. A school spends...

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

Correct answer

40

Step-by-step solution

13x+17y=1000017x+13y=10000+a\begin{aligned} & 13 x+17 y=10000 \\ & 17 x+13 y=10000+a\end{aligned} A pen costs Rs. 13 and a note book costs Rs. 17. A school spends exactly Rs. 10000 in the year 2017-18 to buy x pens
x=10000−17y13y=329x=339⇒10040\begin{aligned} & x=\frac{10000-17 y}{13} \\ & y=329 \\ & x=339 \\ & \Rightarrow 10040\end{aligned}
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