Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 8 Comparing Quantities Ex 8.2 Textbook Exercise Questions and Answers.
PSEB Solutions for Class 8 Maths Chapter 8 Comparing Quantities Ex 8.2
1. A man got a 10% increase in his salary. If his new salary is ₹ 1,54,000, find his original salary.
Solution:
Let the original salary be ₹ 100.
After 10% increase, the new salary = ₹ (100 + 10)
= ₹ 110
If his new salary is ₹ 110,
then the original salary = ₹ 100
If new salary is ₹ 1,54,000,
then original salary = (\(\frac {100}{110}\) × 1,54,000)
= 100 × 1400
= ₹ 140000
Thus, his original salary was ₹ 1,40,000.
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?
Solution:
Number of people went to the zoo on Sunday = 845
Number of people went to the zoo on Monday = 169
∴ Decrease in the number of people visiting the zoo on Monday = (845 – 169) = 676
Percentage decrease = \(\left(\frac{\text { Decrease }}{\text { Original number }} \times 100\right) \%\)
= (\(\frac {676}{845}\) × 100) %
= 80 %
Thus, 80% decrease in the number of people visiting the zoo on Monday.
3. A shopkeeper buys 80 articles for ₹ 2400 and sells them for a profit of 16%. Find the selling price of one article.
Solution:
Cost price of 80 articles = ₹ 2400
∴ Cost price of 1 article = ₹ \(\frac {2400}{80}\) = ₹ 30
Profit = 16%
∴ Profit on 1 article = ₹ \(\left(\frac{16}{100} \times 30\right)\)
= ₹ 4.80
∴ Selling price of 1 article
= Cost price + Profit
= ₹ 30 + ₹ 4.80
= ₹ 34.80
Thus, selling price of one article is ₹ 34.80.
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.
Solution:
Cost price of an article = ₹ 15,500
Repair charge (overhead charge) = ₹ 450
∴ Total cost price = Cost price of an article + Overhead expenses
= ₹ (15500 + 450) = ₹ 15,950
Profit per cent = 15%
Amount of profit = 15% of ₹ 15,950
= ₹ \(\left(\frac{15}{100} \times 15950\right)\)
= ₹ \(\left(\frac{23925}{10}\right)\)
= ₹ 2392.50
∴ Selling price = Total cost + Profit
= ₹ (15950 + 2392.50)
= ₹ 18342.50
Thus, the selling price of an article is ₹ 18,342.50.
5. A VCR and TV were bought for ₹ 8000 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.
Solution:
(i) Cost price of a VCR = ₹ 8000,
Loss per cent = 4 %
∴ Loss amount = 4% of cost
= ₹ \(\left(\frac{4}{100} \times 8000\right)\)
= ₹ (4 × 80)
= ₹ 320
∴ Selling price = Cost price – Loss
= ₹ (8000 – 320)
= ₹ 7680
(ii) Cost price of a TV = ₹ 8000
Profit per cent = 8%
∴ Profit amount = 8 % of cost
= ₹ \(\left(\frac{8}{100} \times 8000\right)\)
= ₹ (8 × 80)
= ₹ 640
∴ Selling price = Cost price + Profit
= ₹ (8000 + 640)
= ₹ 8640
Total cost price of a VCR and TV = ₹ (8000 + 8000)
= ₹ 16,000
Total selling price of a VCR and TV = ₹ (7680 + 8640)
= ₹ 16,320
SP > CR
∴ profit = SP – CP
= ₹ (16,320 – 16,000)
= ₹ 320
∴ Profit per cent = \(\left(\frac{\text { Profit }}{\text { Cost price }} \times 100\right) \%\)
= \(\left(\frac{320}{16000} \times 100\right) \%\)
= 2%
Thus, there is 2% profit on the whole transaction.
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 ?
Solution:
MP of a pair of jeans = ₹ 1450
MP of one shirt = ₹ 850
∴ MP of two shirts = ₹ (2 × 850)
= ₹ 1700
∴ Total MP of three items = ₹ (1450 + 1700)
= ₹ 3150
Discount per cent = 10%
∴ Amount of discount = 10% of total cost
= ₹ \(\left(\frac{10}{100} \times 3150\right)\)
= ₹ 315
Bill amount = MP – Discount
= ₹ (3150 – 315)
= ₹ 2835
Thus, customer would have to pay ₹ 2835 for a pair of jeans and two shirts.
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)
Solution:
Let CP of 1st buffalo be ₹ x
Gain (Profit) per cent = 5%
Amount of profit = 5 % of CP
= ₹ \(\left(\frac{5}{100} \times x\right)\)
= ₹ \(\frac{5 x}{100}\)
∴ SP = CP + Profit
= ₹ \(\left(x+\frac{5 x}{100}\right)\)
= ₹ \(\left(\frac{100 x+5 x}{100}\right)\)
= ₹ \(\frac{105 x}{100}\)
But, SP of a buffalo = ₹ 20,000 (Given)
∴ \(\frac{105 x}{100}\) = ₹ 20,000
∴ x = ₹ \(\left(\frac{20000 \times 100}{105}\right)\)
= ₹ 19047.62
Let the cost price of 2nd buffalo = ₹ y
Loss per cent = 10%
Amount of loss = 10% of CP
= ₹ \(\left(\frac{10}{100} \times y\right)\)
= ₹ \(\frac{10 y}{100}\)
SP = CP – Loss
= ₹ \(\left(y-\frac{10 y}{100}\right)\)
= ₹ \(\left(\frac{100 y-10 y}{100}\right)\)
= ₹ \(\frac{90 y}{100}\)
But SP of a buffalo = ₹ 20,000 (Given)
∴ \(\frac{90 y}{100}\) = ₹ 20,000
∴ y = ₹ \(\left(\frac{20000 \times 100}{90}\right)\)
= ₹ 22222.22
Total CP of both buffaloes = ₹ (x + y)
= ₹ (19047.62 + 22222.22)
= ₹ 41,269.84
Total SP of both buffaloes = ₹ (20000 + 20000)
= ₹ 40,000
∴ SP < CP
Amount of loss = CP – SP
= ₹ (41269.84 – 40000)
= ₹ 1269.84
Thus, there is overall loss of ₹ 1269.84.
8. The price of a TV is ₹ 13,000. The GST charged on it is at the rate of 12%. Find the amount that Vinod will have to pay if he buys it.
Solution:
Price of a TV = ₹ 13,000
GST per cent = 12%
∴ Amount of GST = 12% of price
= ₹ \(\left(\frac{12}{100} \times 13,000\right)\)
= ₹ 1560
∴ Total amount = Price of a TV + GST
= ₹ (13,000 + 1560)
= ₹ 14,560
Thus, Vinod will have to pay ₹ 14,560.
9. Aran bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is ₹ 1600, find the marked price.
Solution:
Let the MP of a pair of skates be ₹ x.
Discount per cent = 20%
∴ Amount of discount = 20% of MP
= ₹ \(\left(\frac{20}{100} \times x\right)\)
= ₹ \(\frac{20 x}{100}\)
∴ Selling price = MP – Discount
= ₹ \(\left(x-\frac{20 x}{100}\right)\)
= ₹ \(\left(\frac{100 x-20 x}{100}\right)\)
= ₹ \(\frac{80 x}{100}\)
= ₹ \(\frac{4}{5} x\)
But, SP of a pair of skates = ₹ 1600 (Given).
∴ \(\frac{4}{5} x\) = 1600
∴ x = ₹ \(\left(\frac{1600 \times 5}{4}\right)\)
∴ x = ₹ 2000
Thus, the marked price of a pair of skates is ₹ 2000.
10. I purchased a hair dryer for ₹ 5400 including 18% GST. Find the price before GST was added.
Solution:
Cost price of hair dryer with GST = ₹ 5400
GST per cent = 18%
Let the price of a hair dryer before GST ) was added be ₹ x.
∴ Amount of GST = 18% of x
= ₹ \(\left(\frac{18}{100} \times x\right)\)
= ₹ \(\frac{18 x}{100}\)
∴ Price after adding GST = ₹ \(\left(x+\frac{18}{100} x\right)\)
= ₹ \(\left(\frac{100 x+18 x}{100}\right)\)
= ₹ \(\frac{118 x}{100}\)
But, price after adding GST = ₹ 5400 (Given)
∴ \(\frac{118 x}{100}\) = 5400
∴ x = ₹ \(\left(\frac{5400 \times 100}{118}\right)\)
= ₹ 4576.27
Thus, the price of a hair dryer before adding GST is ₹ 4576.27.
11. An article was purchased for ₹ 1239 including GST of 18%. Find the price of the article before GST was added.
Solution:
Such type of sums can be done by two methods.
One method:
Let the price of an article before adding GST be ₹ 100.
GST = 18%
∴ price including GST = ₹ (100 + 18)
= ₹ 118
If price including GST is ₹ 118,
then price before adding GST = ₹ 100
∴ if price including GST is ₹ 1239,
then price before adding GST = ₹ \(\left(\frac{1239}{118} \times 100\right)\)
= ₹ 1050
Thus, the price of an article before adding GST was ₹ 1050.
Another method:
Let the price of an article before adding GST be ₹ x.
GST = 18%
Amount of GST = 18% of ₹ x
= ₹ \(\left(\frac{18}{100} \times x\right)\)
= ₹ \(\frac{18 x}{100}\)
Price after adding GST = ₹ \(\left(x+\frac{18 x}{100}\right)\)
= ₹ \(\left(\frac{118 x}{100}\right)\)
But, the price of an article = ₹ 1239 (Given)
∴ \(\frac{118 x}{100}\) = 1239
∴ x = ₹ \(\left(\frac{1239 \times 100}{118}\right)\)
= ₹ 1050
Thus, the price of an article before adding GST was ₹ 1050.