Percentages | IT

Question 18

Context: Raghu purchased rice at ₹35 per kg and sold 10 kg of it for ₹300.

Q. Could we have just calculated the loss percentage per kg instead? Would it be the same?

Solution

Understand the Question

Profit and loss percentages are relative measures (ratios), so they remain constant regardless of the total quantity considered.
Calculating the loss percentage on the total quantity gives the exact same result as calculating it on a per-unit (per kg) basis.
To verify this, we compute both:
1. The total loss percentage on the entire $10\text{ kg}$ .
2. The loss percentage on $1\text{ kg}$ .

Step 1 · Calculate Total Loss Percentage

Given cost per kg $= \text{₹}35$ and quantity $= 10\text{ kg}$ : Diagram 1

\begin{aligned} \text{Total CP} &= \text{Cost per kg} \times \text{Quantity} \\[0.6em] &= \text{₹}35 \times 10\text{ kg} \\[0.6em] &= \text{₹}350 \end{aligned}

Given $\text{Total SP} = \text{₹}300$ for $10\text{ kg}$ :

\begin{aligned} \text{Total Loss} &= \text{Total CP} - \text{Total SP} \\[0.6em] &= \text{₹}350 - \text{₹}300 \\[0.6em] &= \text{₹}50 \end{aligned}

Calculating total loss percentage:

\begin{aligned} \text{Loss Percentage} &= \dfrac{\text{Total Loss}}{\text{Total CP}} \times 100 \\[0.6em] &= \dfrac{\text{₹}50}{\text{₹}350} \times 100 \\[0.6em] &= \dfrac{1}{7} \times 100 \\[0.6em] &= \dfrac{100}{7}\% \approx 14.28\% \end{aligned}

Step 2 · Calculate Loss Percentage per kg

Given $\text{CP per kg} = \text{₹}35$ :

\begin{aligned} \text{SP per kg} &= \dfrac{\text{Total SP}}{\text{Quantity}} \\[0.6em] &= \dfrac{\text{₹}300}{10\text{ kg}} \\[0.6em] &= \text{₹}30\text{ per kg} \end{aligned}

Calculating loss per kg:

\begin{aligned} \text{Loss per kg} &= \text{CP per kg} - \text{SP per kg} \\[0.6em] &= \text{₹}35 - \text{₹}30 \\[0.6em] &= \text{₹}5 \end{aligned}

Calculating loss percentage per kg:

\begin{aligned} \text{Loss Percentage per kg} &= \dfrac{\text{Loss per kg}}{\text{CP per kg}} \times 100 \\[0.6em] &= \dfrac{\text{₹}5}{\text{₹}35} \times 100 \\[0.6em] &= \dfrac{1}{7} \times 100 \\[0.6em] &= \dfrac{100}{7}\% \approx 14.28\% \end{aligned}

Answer

Yes, we could have calculated the loss percentage per kg instead, and it would be the same ( $\approx 14.28\%$ or $\dfrac{100}{7}\%$ ). Target percentages do not depend on the quantity.

Common Mistakes

Dividing by Selling Price: Using $\text{SP}$ in the denominator instead of $\text{CP}$ . Loss percentage is always calculated with respect to $\text{CP}$ : $\dfrac{\text{Loss}}{\text{CP}} \times 100$ .
Assuming Scale Changes Percentage: Assuming that since the rupee loss differs ( $₹50$ total vs. $₹5$ per kg), the loss percentage will also differ. Ratios scale proportionally.

More questions in IT

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Complete the following table:

Q10

Context: Kishanlal's daily sales target is ₹5000.

Q. On Days 5 and 6 his sales were ₹7800 and ₹9550 respectively. Calculate the percentage of the target achieved on these days.

Q11

Context: Kishanlal's daily sales target is ₹5000.

Q. On Day 7, he achieved 150% of his target. On Day 8, he achieved 210% of his target. Find the sales made on these days.

Q12

Complete the table below. Mark the approximate locations in the following diagram.

Q13

Complete this table by calculating the percentages to answer the questions:

Which product has a larger share of badam?
Which product uses a smaller proportion of food chemicals?

Q14

Check if the percentages of each product add up to 100.

Q15

Find the profit percentage of the wholesaler and the manufacturer.

Q16

Shambhavi owns a stationery shop. She procures 200 page notebooks at ₹36 per book. She sells them with a profit margin of $20\%$ . Find the selling price.

Q17

She sells crayon boxes at ₹50 per box with a profit margin of 25%. How much did Shambhavi buy them from the wholesaler?

Q18

Context: Raghu purchased rice at ₹35 per kg and sold 10 kg of it for ₹300.

Q. Could we have just calculated the loss percentage per kg instead? Would it be the same?

Q19

Context: Shyamala had procured decorative vases at ₹2650 per piece. One of the pieces was slightly damaged. She decides to sell it at a loss of 18%.

Q. Try making an estimate. Draw a rough diagram depicting the given situation.

Q20

Due to heavy rains, Snehal could not transport strawberries to Hyderabad from his farm in Panchgani. He sells some of his stock at ₹80 per kg with a $12\%$ loss. What is the cost price?

Q21

A utensil store is offering a $35\%$ discount on the cooker with an MRP $\text{₹}1800$ . What is the selling price? If the cost price was $\text{₹}900$ , what is the percentage profit made after the sale?

Q22

Check if the calculations are correct in the bill shown.

Q23

You may share any bills you have at home with the class. Observe the different elements present in the bills. Are there any similarities or differences in these bills?

Q24

Suppose we want to know the expression/formula to find the total interest amount gained at the end of the maturity period. What would be the formula for each of the two options?

Q25

Tricky Percentages

Would You Rather?

You have won a contest. The organisers offer you two options to choose from: Option A: You deposit ₹100 and you get back ₹300. Option B: You deposit ₹1000 and you get back ₹1500. What is the percentage gain each option gives? You can choose any option only once. Which option would you choose? Why?

Q26

A provision store is offering a stock clearance sale. Customers can choose one of the two options — 20% discount or ₹50 discount—for any purchase above ₹150. Which option would you choose if you want to:

(i) buy items worth ₹180 (ii) buy items worth ₹225 (iii) buy items worth ₹300

Q27

Ariba and Arun have some marbles. Ariba says, “The number of marbles with me is 120% of the marbles Arun has”. What would be an appropriate statement Arun could make comparing the number of marbles he has with Ariba’s?