DAV Class 8 Maths Chapter 5 Brain Teasers

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DAV Class 8 Maths Chapter 5 Brain Teasers

Profit, Loss & Discount Brain Teasers


1. A. Tick (✓) the correct option.

(a) If the selling price of an article is twice the cost price, the profit per cent is—

\( \begin{aligned} (i)\ &\ 50\% \\[5pt] (ii)\ &\ 100\% \\[5pt] (iii)\ &\ 150\% \\[5pt] (iv)\ &\ 200\% \end{aligned} \)

Solution

\[ \begin{aligned} \text{Let C.P} &= \text{₹}\,100 \\ \text{S.P} &= 2\times 100 \implies \text{₹}\,200 \\ \text{Profit} &= 200-100 \implies \text{₹}\,100 \\[6pt] \color{green}\text{Profit }\% &= \color{green}\dfrac{100}{100}\times 100 \\[6pt] & \implies 100\% \end{aligned} \]

Answer \( {\color{orange}(ii)}\ \color{red}{100\%} \)

(b) A jeans is marked for ₹ 2,590, but is sold for ₹ 2,331, then discount % is—

\( \begin{aligned} (i)\ &\ 20\% \\[5pt] (ii)\ &\ 15\% \\[5pt] (iii)\ &\ 10\% \\[5pt] (iv)\ &\ 5\% \end{aligned} \)

Solution

\[ \begin{aligned} \text{M.P}&=\text{₹}\,2590 \\ \text{S.P}&=\text{₹}\,2331 \\[6pt] \color{green} \text{Discount} &= 2590-2331 \\ &= \text{₹}\,259 \\[4pt] \color{green} \text{Discount }\% &= \frac{259}{2590}\times 100 \\[6pt] &=\frac{\cancel{259}^{\,1}}{\cancel{2590}_{\ 10}}\times 100 \\[6pt] &= 10\% \end{aligned} \]

Answer \( {\color{orange}(iii)}\ \color{red}{10\%} \)

(c) If selling price of five pens is equal to the cost price of four pens, then the gain or loss% is—

\( \begin{aligned} (i)\ &\ 20\% \text{ gain} \\[5pt] (ii)\ &\ 20\% \text{ loss} \\[5pt] (iii)\ &\ 25\% \text{ loss} \\[5pt] (iv)\ &\ 25\% \text{ gain} \end{aligned} \)

Solution

\[ \begin{aligned} \text{Let C.P of 1 pen} &= \text{₹}\,1 \\ \text{C.P of 5 pen} &= \text{₹}\,5 \\ \text{S.P of 5 pen} &= \text{₹}\,4 \\[5pt] \color{green} \text{Loss} &= 5 - 4 \\ &=1 \\ \\ \color{green}\text{Loss }\% &= \frac{1}{5}\times 100 \\[5pt] &= 20\% \end{aligned} \]

Answer \( {\color{orange}(ii)}\ \color{red}{20\% \text{ loss}} \)

(d) Selling price of shoes is ₹ 420 including 5% GST. The original price of the shoes is—

\( \begin{aligned} (i)\ &\ \text{₹}\,442 \\[5pt] (ii)\ &\ \text{₹}\,400 \\[5pt] (iii)\ &\ \text{₹}\,401.50 \\[5pt] (iv)\ &\ \text{₹}\,420 \end{aligned} \)

Solution

\[ \begin{aligned} \text{Original price} &= \frac{\text{S.P}\times 100}{100+\text{GST}\%} \\[6pt] &= \frac{\cancel{420}^{4} \times 100}{\cancel{105}_1} \\[6pt] &= 4\times 100 \\ &=\text{₹}\,400 \end{aligned} \]

Answer \( {\color{orange}(ii)}\ \color{red}{\text{₹}\,400} \)

(e) Discount is always calculated on—

\( \begin{aligned} (i)\ &\ \text{cost price} \\[5pt] (ii)\ &\ \text{marked price} \\[5pt] (iii)\ &\ \text{selling price} \\[5pt] (iv)\ &\ \text{GST} \end{aligned} \)

Answer \( {\color{orange}(ii)}\ \color{red}{\text{marked price}} \)

B. Answer the following questions.

(a) After giving a discount of 8% on the marked price, an article was sold for ₹ 414. Find the marked price of the article.

Solution

\[ \begin{aligned} \text{S.P} &= \text{₹}\,414 \\ D\% &= 8\% \\[6pt] \color{green}\text{M.P} &= \color{green}\frac{\text{S.P}\times 100}{100-D\%} \\[6pt] &= \frac{414\times 100}{100-8} \\[6pt] &= \frac{\cancel{414}^{18} \times \cancel{100}^{25}}{\cancel{92}_{\cancel{23}_1}} \\[6pt] &= 18\times 25 \\ \text{M.P} &=\text{₹}\,450 \end{aligned} \]

Answer Marked price \(=\ \color{red}{\text{₹}\,450}\)

(b) A fan is sold for ₹ 650. The gain is one-fourth of the cost price of the fan. Find the gain per cent.

Solution

\[ \begin{aligned} \text{Let C.P} &= x \\[6pt] \text{Profit} &= \frac{x}{4} \\[4pt] \color{green}\text{C.P}+\text{Profit} &= \color{green}\text{S.P} \\[6pt] x+\frac{x}{4} & = 650\\[6pt] \frac{5x}{4} & = 650\\[6pt] x & =\frac{650\times 4}{5}\\[6pt] x &= \text{₹}\,520 \\[6pt] \color{green}CP &= \text{₹}\,520 \\[6pt] \color{green}\text{Profit} &= \frac{520}{4} \implies \text{₹}\,130 \\[4pt] \color{green}\text{Profit }\% &= \frac{\cancel{130}^{1}}{\cancel{520}_{4}}\times 100 \\[6pt] &= \frac{100}{4}\\[6pt] &=25\% \end{aligned} \]

Answer Gain \(=\ \color{red}{25\%}\)

(c) A shopkeeper buys pencils at 10 for ₹ 10 and sells them at 8 for ₹ 10. Find the profit per cent.

Solution

\[ \begin{aligned} \text{C.P of 10 pencils} &= \text{₹}\,10 \\ \text{C.P of 1 pencil } &= \text{₹}\,1 \\[6pt] \text{S.P of 8 pencils} &= \text{₹}\,10 \\[6pt] \text{S.P of 1 pencil} &= \frac{10}{8}\\[6pt] & \implies \text{₹}\,1.25 \\[6pt] \text{Profit} &= 1.25-1\\[6pt] & = 0.25 \\[4pt] \color{green}\text{Profit }\% &= \frac{0.25}{1}\times 100 \\[6pt] &= 25\% \end{aligned} \]

Answer Profit \(=\ \color{red}{25\%}\)

(d) Find the rate of GST if an article marked at ₹ 5,000 is sold for ₹ 5,900.

Solution

\[ \begin{aligned} \text{M.P} &= \text{₹}\,5000 \\ \text{S.P (incl. GST)} &=\text{₹}\,5900 \\[6pt] GST & = 5900 - 5000 \\ GST & = 900 \\[6pt] \color{green}\text{GST} \% &= \frac{900}{5000} \times 100\\[6pt] &= \frac{90}{5}\\[6pt] &= 18\% \end{aligned} \]

Answer GST% \(=\ \color{red}{18\%}\)

(e) A person pays ₹ 2,800 for a cooler marked at ₹ 3,500. Find the discount per cent offered.

Solution

\[ \begin{aligned} \text{M.P} &= \text{₹}\,3500 \\ \text{S.P} &= \text{₹}\,2800 \\[4pt] \color{green}\text{Discount} &= \color{green}\text{M.P}-\text{S.P} \\ &= 3500-2800\\ &=\text{₹}\,700 \\[6pt] \color{green}\text{Discount }\% & = \color{green} \frac{Discount}{MP}\times 100 \\[6pt] & = \frac{\cancel{700}^{1}}{\cancel{3500}_{5}}\times 100 \\[6pt] &= \frac{100}{5} \\[6pt] &=20\% \end{aligned} \]

Answer Discount \(=\ \color{red}{20\%}\)

2. Rajan purchased a purse at 25% discount on its marked price but sold it at the marked price. Find the gain per cent of Rajan on this transaction.

Solution

\[ \begin{aligned} \text{Let M.P} &= \text{₹}\,100 \\[4pt] D\% &= 25\% \\[4pt] \color{green}\text{C.P} &= \color{green}\frac{\text{M.P}\times(100-D\%)}{100} \\[6pt] &= \frac{100\times(100-25)}{100} \\[6pt] &= \frac{\cancel{100} \times 75}{\cancel{100}} \\[6pt] CP &= \text{₹}\,75 \\[6pt] \color{green}\text{S.P} &= \color{green}\text{sold at M.P} \\[6pt] SP &= \text{₹}\,100 \\[6pt] \color{green} \text{Profit} &= \color{green}\text{S.P}-\text{C.P}\\[6pt] &=100-75 \\[6pt] \text{Profit} &=\text{₹}\,25 \\[6pt] \color{green}\text{Profit }\% &= \color{green}\frac{\text{Profit}}{\text{C.P}}\times 100 \\[6pt] &= \frac{\cancel{25}^{1}}{\cancel{75}_{3}}\times 100 \\[6pt] &= \frac{100}{3} \\[6pt] \color{green}\text{Profit }\% &= 33\frac{1}{3}\% \end{aligned} \]

Answer Rajan’s gain% \(=\ \color{red}{33\dfrac{1}{3}\%}\)

3. Jasleen marks her goods at 30% above the cost price and allows a discount of 25% on the marked price. Find her gain or loss per cent.

Solution

\[ \begin{aligned} \text{Let C.P} &= \text{₹}\,100 \\[6pt] MP & = 30\%\text{ above C.P}\\[6pt] \color{green}\text{M.P} &= \frac{100\times(100+30)}{100} \\[6pt] &= \frac{\cancel{100} \times 130}{\cancel{100}} \\[6pt] MP &= \text{₹}\,130 \\[8pt] D\% &= 25\% \\[6pt] \color{green}\text{S.P} &= \color{green}\frac{\text{M.P}\times(100-D\%)}{100} \\[6pt] &= \frac{130\times (100 - 25)}{100}\\[6pt] &= \frac{130\times \cancel{75}^3}{\cancel{100}_4}\\[6pt] &= \frac{390}{4} \\[6pt] SP&= \text{₹}\,97.5 \\[8pt] \color{green}\text{Loss} &= 100-97.5\\ &=\text{₹}\,2.5 \\[6pt] \color{green}\text{Loss }\% &= \frac{2.5}{100}\times 100\\[6pt] &=2.5\% \end{aligned} \]

Answer Loss % \( = \color{red}{2.5\% }\)

4. How much per cent above the cost price should a shopkeeper mark his goods so that after allowing a discount of 20% on the marked price, he gains 12%?

Solution

\[ \begin{aligned} \text{Let C.P} &= \text{₹}\,100 \\[6pt] \text{Gain } \% &= 12\% \\[6pt] \color{green}\text{S.P} &= \color{green}\frac{\text{C.P}\times(100+\text{P}\%)}{100}\\[6pt] &= \frac{\cancel{100} \times (100+12)}{\cancel{100}} \\[6pt] SP&= \text{₹}\,112 \\[6pt] D\% &= 20\% \\[6pt] \color{green}\text{M.P} &= \color{green}\frac{\text{S.P}\times100}{100-D\%} \\[6pt] &= \frac{112\times100}{100-20} \\[6pt] &= \frac{11200}{80}\\[6pt] MP&= \text{₹}\,140 \\[6pt] \color{green}\text{Required Mark-up }\% &= \color{green}\frac{\text{M.P}-\text{C.P}}{\text{C.P}}\times100\\[6pt] &= \frac{140-100}{100}\times 100 \\[6pt] &= \frac{40}{\cancel{100}}\times \cancel{100} \\[6pt] \color{green}\text{Required Percentage}&= 40\% \end{aligned} \]

Answer He should mark the goods \( \color{red}{40\%} \) above the cost price.

5. Rohit marks his goods at 40% above the cost price but allows a discount of 5% for cash payment. What actual profit does he make, if he receives ₹ 1,064 after allowing the discount?

Solution

\[ \begin{aligned} \text{S.P} &= \text{₹}\,1064 \\[6pt] \text{D} \% &= 5\% \\[6pt]\color{green}\text{M.P} &= \color{green}\frac{\text{S.P}\times 100}{100-D\%}\\[6pt] &= \frac{1064 \times 100}{100-5} \\[6pt] &= \frac{\cancel{1064}^{56} \times \cancel{100}^{20}}{\cancel{95}_{\cancel{19}_1}} \\[6pt] &= 56 \times 20 \\[6pt] \color{green} MP &= \text{₹}\,1120 \\[2pt] \text{P}\% &= 40\% \\[6pt] \color{green}\text{C.P} &= \color{green}\frac{\text{M.P}\times 100}{100+P\%} \\[6pt] & = \frac{1120 \times 100}{100 + 40} \\[6pt] & = \frac{\cancel{1120}^8 \times 100}{\cancel{140}_1} \\[6pt] \color{green} CP & = \text{₹}\,800 \\[10pt] \color{green}\text{Actual Profit} &= \color{green}\text{S.P}-\text{C.P} \\[6pt] &= 1064-800 \\[6pt] \color{green}\text{Actual Profit} &= \text{₹}\,264 \end{aligned} \]

Answer Actual Profit \(=\ \color{red}{\text{₹}\,264}\)

6. Mr Kumar went shopping. Mrs Kumar bought a saree for ₹ 12,500, clothes for the kids for ₹ 9,280 and shirts for Mr Kumar for ₹ 10,445. If GST charged on the purchases is 12%, what is the total amount that Mr Kumar has paid?

Solution

\[ \begin{aligned} \text{Total CP} &= 12500 + 9280 + 10445 \\ &= \text{₹}\,32225 \\[8pt] \text{GST } \% &= 12\% \\[8pt] \text{GST Amount }& = \frac{\cancel{12}^3}{\cancel{100}_{\cancel{25}_1}} \times \cancel{32225}^{1289} \\[6pt] &= 3 \times 1289 \\ &= \text{₹}\,3867 \\[8pt] \color{green}\text{Total Amount Paid} &= \color{green}\text{CP} + \text{GST} \\ &= 32225 + 3867 \\ &= \text{₹}\,36092 \end{aligned} \]

Answer Mr Kumar paid a total of \( \color{red}{\text{₹}\,36092} \)

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