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Mathematics · 2023 · 4 marks
CBSE 2023 · Region 6 · Set 1 · Q36
A coaching institute of Mathematics conducts classes in two batches I and II and fees for rich and poor children are different. In batch I, there are…
A coaching institute of Mathematics conducts classes in two batches I and II and fees for rich and poor children are different. In batch I, there are $\displaystyle 20$ poor and $\displaystyle 5$ rich children, whereas in batch II, there are $\displaystyle 5$ poor and $\displaystyle 25$ rich children. The total monthly collection of fees from batch I is ₹ $\displaystyle 9000$ and from batch II is ₹ $\displaystyle 26$,000. Assume that each poor child pays ₹ $\displaystyle x$ per month and each rich child pays ₹ y per month.
Based on the above information, answer the following questions :
(i)
Represent the information given above in terms of $\displaystyle x$ and y .
(ii)
Find the monthly fee paid by a poor child.
OR Find the difference in the monthly fee paid by a poor child and a rich child.
(iii)
If there are $\displaystyle 10$ poor and $\displaystyle 20$ rich children in batch II, what is the total monthly collection of fees from batch II ?
Marking-scheme solution
(i)
$\displaystyle 20 x+5 y=9000$
$\displaystyle 5 x+25 y=26000$
(ii)
Solving the equations $\displaystyle \mathrm{x}=200$
Monthly fee paid by poor child $\displaystyle =₹ 200$
OR
(ii)
getting $\displaystyle \mathrm{x}=200$ and $\displaystyle \mathrm{y}=1000$
Difference in the fee $\displaystyle =1000-200=₹ 800$
(iii)
\[\begin{aligned}
10 x+20 y & =10(200)+20(1000) \\
& =₹ 22000
\end{aligned}
\]
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