DAV Class 8 Maths Chapter 5 Worksheet 3
Profit, Loss & Discount Worksheet 3
1. Rehana purchased a dress for ₹ 5,400 including 12% GST. Find the price of the dress before GST was added.
Solution
\[ \begin{align*} \text{Total Price (including GST)} &= \text{₹ } 5400 \\ \text{GST }\% &= 12\% \\ \text{Let the price before GST was added} &= x \\ \\ x + 12\% \text{ of } x &= 5400 \\ \\ x + \frac{12x}{100} &= 5400 \\ \\ \frac{100x + 12x}{100} &= 5400 \\ \\ \frac{112x}{100} &= 5400 \\ \\ x & = \frac{{\cancel{5400}}^{\color{brown}1350} \times {{\cancel{100}}^{\color{blue}25}}}{{{\cancel{112}}_{\cancel{\color{blue}28}}}_{\color{brown}7}} \\ \\ x & = \frac{1350 \times 25}{7} \\ \\ x & = \frac{33750}{7} \\ \\ x & = \text{₹ }4821.42 \end{align*} \]
Answer The price of the dress before GST was added \( = \color{red} \text{₹} 4821.42 \)
2.
Find the amount to be paid for the following items if 28% GST is charged on each item.
(i) A chocolate at ₹ 150.
(ii) A laptop at ₹ 55,000.
(iii) A perfume bottle at ₹ 580.
Solution
(i) A chocolate at ₹ 150 \[ \begin{align*} \text{Price of chocolate} &= \text{₹} 150 \\ \text{GST } \% &= 28\% \\ \\ \text{GST Amount} & = 28\% \text{ of } 150 \\ \\ &= \frac{{\cancel{28}}^{\color{brown}14}}{{{\cancel{100}}_{\cancel{\color{blue}2}}}_{\color{brown}1}} \times {\cancel{150}}^{\color{blue}3} \\ \\ &= 14 \times 3 \\ \\ &= \text{₹} 42 \\ \\ \text{Total Amount} &= \text{₹} 150 + \text{₹} 42 \\ &= \text{₹} 192 \end{align*} \]
Answer The total amount to be paid for the chocolate \( = \color{red} \text{₹} 192 \)
(ii) A laptop at ₹ 55000
\[ \begin{align*} \text{Price of laptop} &= \text{₹} 55000 \\ \text{GST }\% &= 28\% \\ \\ \text{GST Amount} &= 28\% \text{ of } 55000 \\ \\ & = \frac{28}{\cancel{100}_1} \times \cancel{55000}^{550} \\ \\ &= 28 \times 550 \\ &= \text{₹} 15400 \\ \\ \text{Total Amount} &= \text{₹} 55000 + \text{₹} 15400 \\ &= \text{₹} 70400 \end{align*} \]Answer The total amount to be paid for the laptop \( = \color{red} \text{₹} 70400 \)
(iii) A perfume bottle at ₹ 580
\[ \begin{align*} \text{Price of perfume bottle} &= \text{₹} 580 \\ \text{GST Percentage} &= 28\% \\ \\ \text{GST Amount} &= 28\% \text{ of } 580\\ & = \frac{28}{100} \times 580 \\ \\ &= \frac{16240}{100} \\ \\ &= \text{₹} 162.40 \\ \\ \text{Total Amount} &= \text{₹} 580 + \text{₹} 162.40 \\ &= \text{₹} 742.40 \end{align*} \]Answer The total amount to be paid for the perfume bottle \( = \color{red} \text{₹} 742.40 \)
3. Raman purchased insecticides for his farm at ₹ 23,600 including GST. If the cost price of the insecticides was ₹ 20,000, how much GST (in %) has he paid?
Solution
\[ \begin{align*} \text{Cost including GST} &= \text{₹ } 23600 \\ \text{Cost Price before GST } (C.P) &= \text{₹ } 20000 \\ \\ \text{GST } &= 23600 - 20000 \\ &= \text{₹} 3600 \\ \\ \text{GST } \% &= \frac{\text{GST }}{\text{C.P}} \times 100 \\ \\ &= \frac{3600}{20000} \times 100 \\ \\ &= \frac{36}{2} \\ \\ \text{GST } \% &= 18\% \\ \end{align*} \]
Answer The GST paid by Raman \( = \color{red} 18\% \)