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Mathematics · 2026 · 5 marks
CBSE 2026 · Region 4 · Set 1 · Q32
(a) A person on tour has ₹ 5,400 for his expenses. If he extends his tour by 5 days, he has to cut down his daily expenses by ₹ 180. Find the…
(a)
A person on tour has ₹ $\displaystyle 5{,}400$ for his expenses. If he extends his tour by $\displaystyle 5$ days, he has to cut down his daily expenses by ₹ $\displaystyle 180$ . Find the original duration of the tour and daily expense.
OR
(b)
The total cost of certain piece of cloth was ₹ $\displaystyle 2$,100. During special sale time, the shopkeeper offered $\displaystyle 2$ m extra cloth for free thus reducing the price of cloth per metre by ₹ $\displaystyle 120$ . What was the original per metre price of cloth and its length?
Marking-scheme solution
Let original duration of the tour be \(\displaystyle x\) days.
∴ Daily expense is ₹ \(\displaystyle \frac{5400}{x}\)
According to the question,
\(\displaystyle \frac{5400}{x}-\frac{5400}{x+5}=180\)
\(\displaystyle \Rightarrow x^{2}+5 x-150=0\)
\(\displaystyle \Rightarrow(x+15)(x-10)=0\)
\(\displaystyle \Rightarrow \mathrm{x}=-15,10\)
\(\displaystyle \because x \neq-15\)
\(\displaystyle \therefore x=10\)
∴ Original duration of tour is $\displaystyle 10$ days and daily expense is ₹ 540.
Let the original length of cloth be \(\displaystyle x\) metre.
∴ Original cost is ₹ \(\displaystyle \frac{2100}{x}\) per metre.
According to the question,
\(\displaystyle \frac{2100}{x}-\frac{2100}{x+2}=120\)
\(\displaystyle \Rightarrow x^{2}+2 x-35=0\)
\(\displaystyle \Rightarrow(x+7)(x-5)=0\)
\(\displaystyle \Rightarrow \mathrm{x}=-7,5\)
\(\displaystyle \because x \neq-7\)
\(\displaystyle \therefore x=5\)
∴ The original price of cloth per metre is ₹$\displaystyle 420$ and original length is $\displaystyle 5$ m.
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