GSEB Class 8 Maths Solutions Chapter 8 Comparing Quantities Exercise 8.2

Question 1. A man got a 10% increase in his salary. If his new salary is ₹ 1,54,000, find his original salary?
Answer: Let the initial salary be \( Rs. x \).
The increase in salary is 10% of \( Rs. x \).
So, the increase amount is \( \frac{10}{100}x = \frac{x}{10} \).
The new salary equals the original salary plus the increase, which is \( x + \frac{x}{10} = \frac{11}{10}x \).
We are given that the new salary is \( Rs. 1,54,000 \).

\( \implies \frac{11}{10}x = 154000 \)
To find \( x \), we multiply \( 154000 \) by \( 10 \) and divide by \( 11 \).
So, \( x = \frac{154000 \times 10}{11} = 1,40,000 \).
Therefore, the person's initial salary was \( Rs. 1,40,000 \).
In simple words: A man got a 10% raise. If his new pay is Rs. 1,54,000, his old pay was Rs. 1,40,000.

Exam Tip: When dealing with percentage increase, remember to add the increase to the original amount to get the new amount. For decrease, subtract it.

Question 2. On Sunday 845 people went to the Zoo. On Monday only 169 people went. What is the per cent decrease in the people visiting the Zoo on Monday?
Answer: On Sunday, the number of visitors was 845.
On Monday, the number of visitors was 169.
The reduction in the number of visitors is \( 845 - 169 = 676 \).
To calculate the percentage decrease, we divide the decrease by the original number of visitors and multiply by 100%.

\( \implies \) Per cent decrease = \( \frac{676}{845} \times 100\% \)
\( = (0.8 \times 100)\% = 80\% \).
So, there was an 80% decrease in the number of people visiting the Zoo on Monday compared to Sunday.
In simple words: 845 people visited on Sunday, but only 169 on Monday. This means there was an 80% drop in visitors.

Exam Tip: Percentage decrease is always calculated based on the original quantity. Make sure to identify the base value correctly.

Question 3. A shopkeeper buys 80 articles for ₹ 2,400 and sells them for a profit of 16%. Find the selling price of one article?
Answer: The cost price of 80 articles is \( Rs. 2400 \).
The shopkeeper makes a profit of 16% on this cost.
Profit amount = 16% of \( Rs. 2400 = \frac{16}{100} \times 2400 \).
This calculates to \( Rs. 16 \times 24 = Rs. 384 \).
The total selling price of 80 articles is the cost price plus the profit.

\( \implies \) Total selling price = \( Rs. 2400 + Rs. 384 = Rs. 2784 \).
To find the selling price of a single article, we divide the total selling price by the number of articles.
Selling price per article = \( Rs. 2784 \div 80 \).
This gives \( Rs. 34.80 \).
In simple words: A shopkeeper bought 80 items for Rs. 2,400 and sold them for a 16% profit. Each item was sold for Rs. 34.80.

Exam Tip: Always read carefully whether the question asks for the total selling price or the selling price per unit. Also, remember to add profit to cost price to get selling price.

Question 4. The cost of an article was ₹ 15,500. ₹ 450 were spent on its repairs. If it is sold for a profit of 15%, find the selling price of the article?
Answer: The initial cost of the article was \( Rs. 15,500 \).
Additionally, \( Rs. 450 \) were spent on its maintenance (overhead expenses).
The total cost of the article (including repairs) is \( Rs. 15500 + Rs. 450 = Rs. 15950 \).
The article is then sold for a profit of 15% on this total cost.
Profit amount = 15% of \( Rs. 15950 = \frac{15}{100} \times 15950 \).
This simplifies to \( \frac{3}{20} \times 15950 = \frac{3 \times 1595}{2} \).
So, the profit is \( Rs. \frac{4785}{2} = Rs. 2392.50 \).
The selling price is the total cost plus the profit.

\( \implies \) Selling price = \( Rs. 15950 + Rs. 2392.50 = Rs. 18342.50 \).
In simple words: An item cost Rs. 15,500, plus Rs. 450 for repairs. If it sold with a 15% profit, the selling price was Rs. 18,342.50.

Exam Tip: Remember that "overhead expenses" or "repair costs" are added to the original cost price to find the total effective cost price before calculating profit or loss.

Question 5. A VCR and TV were bought for ₹ 8,000 each. The shopkeeper made a loss of 4% on the VCR and a profit of 8% on the TV. Find the gain or loss per cent on the whole transaction?
Answer: For the VCR:
The cost price (CP) of the VCR was \( Rs. 8000 \).
A loss of 4% was made on the VCR.
Loss amount = 4% of \( Rs. 8000 = \frac{4}{100} \times 8000 = Rs. 320 \).
The selling price (SP) of the VCR = \( Rs. 8000 - Rs. 320 = Rs. 7680 \).
For the TV:
The cost price (CP) of the TV was \( Rs. 8000 \).
A profit of 8% was made on the TV.
Profit amount = 8% of \( Rs. 8000 = \frac{8}{100} \times 8000 = Rs. 640 \).
The selling price (SP) of the TV = \( Rs. 8000 + Rs. 640 = Rs. 8640 \).
Now, let's look at the whole transaction:
Total Cost Price (CP) = CP of VCR + CP of TV = \( Rs. 8000 + Rs. 8000 = Rs. 16000 \).
Total Selling Price (SP) = SP of VCR + SP of TV = \( Rs. 7680 + Rs. 8640 = Rs. 16320 \).
We compare the total SP with the total CP.

\( \implies \) Total SP (\( Rs. 16320 \)) is greater than Total CP (\( Rs. 16000 \)). This means there is an overall profit.
Overall profit = Total SP - Total CP = \( Rs. 16320 - Rs. 16000 = Rs. 320 \).
To find the overall profit percentage, we use the formula: \( \frac{\text{Overall Profit}}{\text{Total CP}} \times 100\% \).
Overall profit per cent = \( \frac{320}{16000} \times 100\% = 2\% \).
In simple words: A shopkeeper bought a VCR and a TV, each for Rs. 8,000. He lost 4% on the VCR but gained 8% on the TV. Overall, he made a 2% profit on everything he sold.

Exam Tip: For overall gain/loss percentage, always calculate the total cost price and total selling price for all items, then apply the percentage formula to the totals.

Question 6. During a sale, a shop offered a discount of 10% on the marked prices of all the items. What would a customer have to pay for a pair of jeans marked at ₹ 1450 and two shirts marked at ₹ 850 each?
Answer: First, let's calculate for the pair of Jeans:
The marked price of the jeans is \( Rs. 1450 \).
The discount offered is 10%.
Discount amount = 10% of \( Rs. 1450 = \frac{10}{100} \times 1450 = Rs. 145 \).
The sale price of the jeans = Marked price - Discount = \( Rs. 1450 - Rs. 145 = Rs. 1305 \).
Next, let's calculate for the two Shirts:
The marked price of one shirt is \( Rs. 850 \).
For two shirts, the marked price is \( Rs. 850 \times 2 = Rs. 1700 \).
The discount offered is 10%.
Discount amount = 10% of \( Rs. 1700 = \frac{10}{100} \times 1700 = Rs. 170 \).
The sale price of the two shirts = Marked price - Discount = \( Rs. 1700 - Rs. 170 = Rs. 1530 \).
Finally, the total amount the customer has to pay is the sum of the sale prices of the jeans and the shirts.
Total sale price = \( Rs. 1305 + Rs. 1530 = Rs. 2835 \).
Therefore, the customer would need to pay \( Rs. 2835 \).
In simple words: A shop had a 10% sale. Jeans cost Rs. 1450 and two shirts cost Rs. 850 each before discount. The customer would pay Rs. 2835 in total after the discount.

Exam Tip: When multiple items are involved, calculate the discounted price for each item or group of items separately, then sum them up for the total amount payable.

Question 7. A milkman sold two of his buffaloes for ₹ 20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss. (Hint: Find CP of each.)
Answer: Let's find the cost price (CP) for each buffalo.
For the 1st buffalo:
Selling price (SP) = \( Rs. 20,000 \).
Profit = 5%.
The formula to find CP when SP and profit percentage are known is: \( \text{CP} = \frac{100}{100 + \text{Profit} \%} \times \text{SP} \).
So, CP = \( \frac{100}{100 + 5} \times 20,000 \)
CP = \( \frac{100}{105} \times 20,000 = \frac{20}{21} \times 20,000 = Rs. \frac{4,00,000}{21} \approx Rs. 19047.62 \).
For the 2nd buffalo:
Selling price (SP) = \( Rs. 20,000 \).
Loss = 10%.
The formula to find CP when SP and loss percentage are known is: \( \text{CP} = \frac{100}{100 - \text{Loss} \%} \times \text{SP} \).
So, CP = \( \frac{100}{100 - 10} \times 20,000 \)
CP = \( \frac{100}{90} \times 20,000 = \frac{10}{9} \times 20,000 = Rs. \frac{2,00,000}{9} \approx Rs. 22222.22 \).
Now, let's calculate the overall CP and SP:
Total Selling Price (Overall SP) = \( Rs. 20,000 + Rs. 20,000 = Rs. 40,000 \).
Total Cost Price (Overall CP) = CP of 1st buffalo + CP of 2nd buffalo
Overall CP = \( Rs. \frac{4,00,000}{21} + Rs. \frac{2,00,000}{9} \).
To add these fractions, find a common denominator, which is 63.
Overall CP = \( Rs. \frac{3 \times 4,00,000}{63} + Rs. \frac{7 \times 2,00,000}{63} \)
Overall CP = \( Rs. \frac{12,00,000 + 14,00,000}{63} \)
Overall CP = \( Rs. \frac{26,00,000}{63} \approx Rs. 41269.84 \).
Comparing Overall CP and Overall SP:
Overall CP (\( Rs. 41269.84 \)) is greater than Overall SP (\( Rs. 40,000 \)).

\( \implies \) This means there is an overall loss.
Overall loss = Overall CP - Overall SP = \( Rs. 41269.84 - Rs. 40,000 \).
Overall loss = \( Rs. 1269.84 \).
In simple words: A milkman sold two buffaloes for Rs. 20,000 each. He gained 5% on one and lost 10% on the other. His total loss on the whole deal was Rs. 1269.84.

Exam Tip: When given selling price and profit/loss percentage, use the inverse formulas to find the cost price. Always calculate total CP and total SP before determining overall gain or loss.

Question 8. The price of a TV is ₹ 13,000. The sales tax charged on it is at the rate of 12%. Find the amount that Vinod will have to pay if he buys it?
Answer: The cost (sale price) of the TV is \( Rs. 13,000 \).
The rate of sales tax charged is 12%.
Sales tax amount = 12% of \( Rs. 13000 = \frac{12}{100} \times 13000 \).
This calculates to \( Rs. 12 \times 130 = Rs. 1560 \).
The total amount Vinod will have to pay is the TV's price plus the sales tax.

\( \implies \) Bill amount = \( Rs. 13000 + Rs. 1560 = Rs. 14,560 \).
Therefore, Vinod will have to pay \( Rs. 14,560 \) for the TV.
In simple words: A TV costs Rs. 13,000, and there's a 12% sales tax. Vinod will pay Rs. 14,560 in total to buy it.

Exam Tip: Remember that sales tax is always added to the original price to determine the final amount a customer pays.

Question 9. Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is ₹ 1,600, find the marked price?
Answer: Let's assume the marked price is \( Rs. 100 \).
The discount given is 20%.
So, discount amount = 20% of \( Rs. 100 = \frac{20}{100} \times 100 = Rs. 20 \).
The sale price (amount paid after discount) would then be \( Rs. (100 - 20) = Rs. 80 \).
We know that if the sale price is \( Rs. 80 \), the marked price is \( Rs. 100 \).
We need to find the marked price when the sale price is \( Rs. 1600 \).
Using a unitary method, if the sale price is \( Rs. 1600 \), then the marked price will be:
Marked price = \( \frac{100}{80} \times 1600 \).
This calculation gives \( Rs. 2000 \).
In simple words: Arun paid Rs. 1,600 for skates after a 20% discount. This means the original price before the discount was Rs. 2,000.

Exam Tip: When finding the original (marked) price after a discount, consider what percentage of the marked price the sale price represents. For a 20% discount, the sale price is 80% of the marked price.

Question 10. I purchased a hair-dryer for ₹ 5,400 including 8% VAT. Find the price before VAT was added?
Answer: Let's assume the original price of the hair-dryer before VAT was \( Rs. 100 \).
The VAT (Value Added Tax) charged is 8%.
VAT amount = 8% of \( Rs. 100 = \frac{8}{100} \times 100 = Rs. 8 \).
The price including VAT would then be the original price plus the VAT amount.

\( \implies \) Price including VAT = \( Rs. 100 + Rs. 8 = Rs. 108 \).
We know that if the bill amount (price including VAT) is \( Rs. 108 \), the original price is \( Rs. 100 \).
We need to find the original price when the bill amount is \( Rs. 5,400 \).
Using a unitary method, if the bill amount is \( Rs. 5,400 \), then the original price will be:
Original price = \( \frac{100}{108} \times 5400 \).
This simplifies to \( Rs. (100 \times 50) = Rs. 5000 \).
Therefore, the price of the hair-dryer before VAT was added was \( Rs. 5000 \).
In simple words: A hair-dryer cost Rs. 5,400, which already included 8% tax. The price of the hair-dryer before that tax was added was Rs. 5,000.

Exam Tip: When finding the original price before VAT, understand that the given price is 100% + VAT percentage. Use this combined percentage to work backward to the 100% original price.