GSEB Class 7 Maths Solutions Chapter 8 Comparing Quantities Exercise 8.3

Question 1. Tell what is the profit or loss in the following transactions. Also find profit per cent or loss per cent in each case.
(a) Gardening shears bought for Rs. 250 and sold for Rs. 325.
(b) A refrigerate bought for Rs. 12,000 and sold at Rs. 13,500.
(c) A cupboard bought for Rs. 2,500 and sold at Rs. 3,000.
(d) A skirt bought for Rs. 250 and sold at Rs. 150.
Answer:
(a) For gardening shears:
Cost Price (CP) = Rs. 250
Selling Price (SP) = Rs. 325
Since CP \( < \) SP, there is a profit.
Profit = SP – CP = Rs. 325 – Rs. 250 = Rs. 75
Profit % = \( \frac{\text{Profit}}{\text{CP}} \times 100\% = \frac{75}{250} \times 100\% = 30\% \)

(b) For a refrigerator:
Cost Price (CP) = Rs. 12,000
Selling Price (SP) = Rs. 13,500
Since CP \( < \) SP, there is a profit.
Profit = SP – CP = Rs. 13,500 – Rs. 12,000 = Rs. 1,500
Profit % = \( \frac{\text{Profit}}{\text{CP}} \times 100\% = \frac{1500}{12000} \times 100\% = 12.5\% \)

(c) For a cupboard:
Cost Price (CP) = Rs. 2,500
Selling Price (SP) = Rs. 3,000
Since CP \( < \) SP, there is a profit.
Profit = SP – CP = Rs. 3,000 – Rs. 2,500 = Rs. 500
Profit % = \( \frac{\text{Profit}}{\text{CP}} \times 100\% = \frac{500}{2500} \times 100\% = 20\% \)

(d) For a skirt:
Cost Price (CP) = Rs. 250
Selling Price (SP) = Rs. 150
Since CP \( > \) SP, there is a loss.
Loss = CP – SP = Rs. 250 – Rs. 150 = Rs. 100
Loss % = \( \frac{\text{Loss}}{\text{CP}} \times 100\% = \frac{100}{250} \times 100\% = 40\% \)
In simple words: First, compare the buying price and selling price to see if it's a profit or loss. Then, calculate the actual profit or loss amount. Finally, use the profit/loss percentage formula, dividing the profit/loss by the original cost price and multiplying by 100.

Exam Tip: Always state clearly whether it's a profit or loss before calculating the percentage. Remember that both profit percentage and loss percentage are always calculated based on the Cost Price (CP).

Question 2. Convert each part of the ratio to percentage:
(a) 3:1
(b) 2:3:5
(c) 1:4
(d) 1:2:5
Answer:
(a) For ratio 3:1:
Total of the parts = \( 3 + 1 = 4 \)
Percentage of the 1st part = \( \frac{3}{4} \times 100\% = 75\% \)
Percentage of the 2nd part = \( \frac{1}{4} \times 100\% = 25\% \)

(b) For ratio 2:3:5:
Total of the parts = \( 2 + 3 + 5 = 10 \)
Percentage of the 1st part = \( \frac{2}{10} \times 100\% = 20\% \)
Percentage of the 2nd part = \( \frac{3}{10} \times 100\% = 30\% \)
Percentage of the 3rd part = \( \frac{5}{10} \times 100\% = 50\% \)

(c) For ratio 1:4:
Total of the parts = \( 1 + 4 = 5 \)
Percentage of the 1st part = \( \frac{1}{5} \times 100\% = 20\% \)
Percentage of the 2nd part = \( \frac{4}{5} \times 100\% = 80\% \)

(d) For ratio 1:2:5:
Total of the parts = \( 1 + 2 + 5 = 8 \)
Percentage of the 1st part = \( \frac{1}{8} \times 100\% = 12.5\% \)
Percentage of the 2nd part = \( \frac{2}{8} \times 100\% = 25\% \)
Percentage of the 3rd part = \( \frac{5}{8} \times 100\% = 62.5\% \)
In simple words: To change a ratio into percentages, first add all the numbers in the ratio to get the total. Then, for each part, divide that part by the total and multiply the result by 100 to get its percentage.

Exam Tip: The sum of all percentages for the parts of a ratio should always add up to 100%. Use this as a quick check for your calculations.

Question 3. The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.
Answer:
Initial population = 25,000
Decreased population = 24,500
Decrease in population = \( 25,000 - 24,500 = 500 \)
Decrease % = \( \frac{\text{Decrease in population}}{\text{Initial population}} \times 100\% \)
Decrease % = \( \frac{500}{25000} \times 100\% = 2\% \)
In simple words: When the population goes down, you find how much it dropped, and then calculate what percentage that drop is from the original population.

Exam Tip: Remember to always divide the actual decrease by the original (initial) amount when calculating percentage change, not the new (final) amount.

Question 4. Arun bought a car for Rs. 3,50,000. The next year, the price went upto Rs. 3,70,000. What was the percentage of price increase?
Answer:
Initial cost = Rs. 3,50,000
Increased cost = Rs. 3,70,000
Increase in cost = Rs. 3,70,000 – Rs. 3,50,000 = Rs. 20,000
Increase % = \( \frac{\text{Increase}}{\text{Initial cost}} \times 100\% \)
Increase % = \( \frac{20000}{350000} \times 100\% = \frac{40}{7}\% = 5\frac{5}{7}\% \)
In simple words: To find the percentage increase, you calculate how much the price went up, then divide that by the original price, and multiply by 100.

Exam Tip: Expressing percentage increase or decrease as a mixed fraction like \( 5\frac{5}{7}\% \) is often more precise than a decimal if the decimal is non-terminating.

Question 5. I buy a T.V for Rs. 10,000 and sell it at a profit of 20%. How much money do I get for it?
Answer:
Cost Price (CP) of the T.V. = Rs. 10,000
Profit percent = 20%
Profit = 20% of Rs. 10,000 = \( \frac{20}{100} \times 10,000 = \text{Rs. } 2,000 \)
Selling Price (SP) = CP + Profit = Rs. 10,000 + Rs. 2,000 = Rs. 12,000
Thus, the T.V. will be sold for Rs. 12,000.
In simple words: When you sell something for a profit, you first figure out the profit amount based on the percentage, then add that profit to the original cost to get the final selling price.

Exam Tip: Always remember that profit percentage is calculated on the Cost Price (CP) unless stated otherwise. The selling price will always be CP + Profit.

Question 6. Juhi sells a washing machine for Rs. 13,500. She loses 20% in the bargain. What was the price at which she bought it?
Answer:
Selling Price (SP) = Rs. 13,500
Loss % = 20%
Let the Cost Price (CP) be x.
CP – Loss = SP
CP – (20% of CP) = Rs. 13,500
\( CP - \frac{20}{100}CP = 13,500 \)
\( CP (1 - \frac{20}{100}) = 13,500 \)
\( CP (\frac{100-20}{100}) = 13,500 \)
\( CP (\frac{80}{100}) = 13,500 \)
\( CP (\frac{4}{5}) = 13,500 \)
\( CP = 13,500 \times \frac{5}{4} \)
\( CP = 3375 \times 5 \)
\( CP = \text{Rs. } 16,875 \)
Thus, Juhi bought the washing machine for Rs. 16,875.
In simple words: If you know the selling price and the percentage of loss, you can work backwards. If there's a 20% loss, it means the selling price is 80% of the original cost. Use this to find the original cost.

Exam Tip: When given selling price and loss percentage, consider the selling price as (100 - loss%) of the cost price. This allows you to directly calculate CP using a simple equation.

Question 7.
(i) Chalk contains calcium, carbon and oxygen in the ratio 10 : 3 : 12. Find the percentage of carbon in chalk.
(ii) If in a stick of chalk, carbon is 3 g, what is the weight of the chalk stick?
Answer:
(i) The ratio of calcium, carbon and oxygen in mixture is 10 : 3 : 12.
Total of ratios = \( 10 + 3 + 12 = 25 \)
Percentage of carbon in the chalk mixture = \( \frac{3}{25} \times 100\% = 12\% \)

(ii) Let the total weight of the chalk stick be x g.
From part (i), carbon makes up 12% of the chalk mixture.
We are given that carbon is 3 g.
Therefore, 12% of x = 3
\( \frac{12}{100} \times x = 3 \)
\( x = \frac{3 \times 100}{12} \)
\( x = \frac{300}{12} \)
\( x = 25 \)
So, the weight of the chalk stick is 25 g.
In simple words: For part (i), add all ratio parts to get a total, then divide the carbon part by the total and multiply by 100 to find the percentage. For part (ii), use the percentage of carbon you found to figure out the total weight of the chalk stick if you know the weight of carbon.

Exam Tip: Always remember that percentages in ratios are calculated based on the total sum of the ratio parts. For questions involving proportions, set up a clear equation to solve for the unknown quantity.

Question 8. Amina buys a book for Rs. 215 and sells it at a loss of 15%. How much does she sell it for?
Answer:
Cost price of the book (CP) = Rs. 275 (Corrected from OCR's 215 as calculation uses 275)
Loss % = 15%
Loss = 15% of CP = \( \frac{15}{100} \times 275 \)
Loss = \( \frac{4125}{100} \)
Loss = Rs. 41.25
Selling Price (SP) = CP – Loss
SP = Rs. 275 – Rs. 41.25
SP = Rs. 233.75
Thus, Amina will sell the book for Rs. 233.75.
In simple words: When you sell something at a loss, you first calculate the amount of money lost based on the percentage, and then subtract that loss from the original cost to get the final selling price.

Exam Tip: Make sure to correctly identify the cost price and calculate the loss amount accurately before subtracting it from the cost price to find the selling price.

Question 9. Find the amount to be paid at the end of 3 years in each case:
(a) Principal = Rs. 1,200 at 12% p.a.
(b) Principal = Rs. 7,500 at 5% p.a.
Answer:
(a) Here, Principal (P) = Rs. 1,200
Rate (R) = 12% p.a.
Time (T) = 3 years
Simple Interest (I) = \( \frac{P \times R \times T}{100} = \frac{1,200 \times 12 \times 3}{100} \)
Simple Interest (I) = \( \text{Rs. } (12 \times 12 \times 3) = \text{Rs. } 432 \)
Amount = Principal + Interest = Rs. 1,200 + Rs. 432 = Rs. 1,632

(b) Principal (P) = Rs. 7,500
Rate (R) = 5% p.a.
Time (T) = 3 years
Simple Interest (I) = \( \frac{P \times R \times T}{100} = \frac{7,500 \times 5 \times 3}{100} \)
Simple Interest (I) = \( \text{Rs. } (75 \times 5 \times 3) = \text{Rs. } 1,125 \)
Amount = Principal + Interest = Rs. 7,500 + Rs. 1,125 = Rs. 8,625
In simple words: To find the total amount to be paid back, first calculate the simple interest by multiplying the principal, rate, and time, then dividing by 100. After that, add this interest to the original principal amount.

Exam Tip: Clearly write down the values for Principal, Rate, and Time before applying the simple interest formula. Make sure the rate is per annum and time is in years to avoid errors.

Question 10. What rate gives Rs. 280 as interest on a sum of Rs. 56,000 in 2 year?
Answer:
Principal (P) = Rs. 56,000
Rate (R) = ?
Time (T) = 2 years
Interest (I) = Rs. 280
Using the Simple Interest formula: \( I = \frac{P \times R \times T}{100} \)
\( 280 = \frac{56,000 \times R \times 2}{100} \)
To find R, rearrange the formula:
\( R = \frac{280 \times 100}{56,000 \times 2} \)
\( R = \frac{28000}{112000} \)
\( R = \frac{1}{4}\% = 0.25\% \)
Thus, an interest rate of 0.25% p.a. will give the required interest.
In simple words: If you know the interest, principal, and time, you can find the interest rate by rearranging the simple interest formula. Multiply interest by 100, then divide by the product of principal and time.

Exam Tip: When finding an unknown variable like Rate, always write down the simple interest formula and substitute the known values first, then algebraically solve for the unknown to prevent calculation mistakes.

Question 11. If Meena gives an interest of Rs. 45 for one year at 9% rate p.a. What is the sum she has borrowed.
Answer:
Principal (P) = ?
Rate (R) = 9% p.a.
Interest (I) = Rs. 45
Time (T) = 1 year
Using the Simple Interest formula: \( I = \frac{P \times R \times T}{100} \)
\( 45 = \frac{P \times 9 \times 1}{100} \)
To find P, rearrange the formula:
\( P = \frac{45 \times 100}{9 \times 1} \)
\( P = \frac{4500}{9} \)
\( P = \text{Rs. } 500 \)
Therefore, the sum Meena borrowed is Rs. 500.
In simple words: If you know the interest amount, the rate of interest, and the time, you can figure out the original sum of money borrowed. Just multiply the interest by 100, then divide it by the rate and time multiplied together.

Exam Tip: Remember that the Simple Interest formula can be rearranged to find any missing variable (P, R, or T) if the other three are known. Double-check your calculations when isolating the principal.