Solution:
Given, MP = Rs. 2055
Discount percentage = 3
\(\ ⇨ \frac{MP-SP}{MP}×100=3 \)
\(\ ⇨ \frac{2055-SP}{2055}×100=3 \)
\(\ ⇨ 2055-SP=\frac{3}{100}×2055 \)
\(\ ⇨ 2055-61.65=SP \)
\(\ ⇨ SP = 1993.35 \) (Rs.)
Aternative Mathod
Let the SP be \(\ x \)
Here,
discount = 3% of 2055
\(\ = \frac{3}{100}×2055 \)
\(\ = 61.65 \)
Now,
\(\ SP = MP - discount \)
\(\ ⇨ SP = 2055-61.65 \)
\(\ ⇨ SP = 1999.3 \) (Rs.)
⸫ The required SP should be Rs. 69.
2. Suman bought a Mathematics Book for Rs. 190 at a discount of 10%. What was the marked price?
Solution:
Given, SP = Rs. 190
Let the marked price be \(\ x \)
discount = 3% of \(\ x \)
\(\ = \frac{10}{100}×x =\frac{x}{10} \) ...(1)
we know,
discount = MP - SP
\(\ ⇨ \frac{x}{10} = x - 190 \)
\(\ ⇨ 190 = x - \frac{x}{10} \)
\(\ ⇨ 190 = \frac{10x-x}{10} \)
\(\ ⇨ 190 = \frac{9x}{10} \)
\(\ ⇨ 9x = 1900 \)
\(\ ⇨ x = 211.1 \)
⸫ The required Marked price was Rs. 211.10
3. Ramen bought an article for Rs. 630 whose marked price was Rs. 700. What is the percentage of discount he got?
Solution:
Given, SP = Rs. 630 [SP for the trader = CP for Ramen]
MP = Rs. 700
We have,
Percentage of discount \(\ = \frac{MP-SP}{MP}×100 \)
\(\ = \frac{700-630}{700}×100 \)%
\(\ = \frac{70}{7} \)%
\(\ = 10 \)%
4. The marked price of a Sofa set is Rs. 30000. On occasion of new year, the shopkeeper sold it at Rs. 25000. What is the percentage of discount?
Solution:
Given, MP = Rs. 30000
SP = Rs. 25000
We have,
Percentage of discount \(\ = \frac{MP-SP}{MP}×100 \)
\(\ = \frac{30000-2500}{30000}×100 \)%
\(\ = \frac{5000}{300} \)%
\(\ = 16.7 \)%
5. After a discount of 10%, a fan is sold at Rs. 1260. What was the marked price of the fan?
Solution:
Given, SP = Rs. 1260
Discount percentage = 10
\(\ ⇨ \frac{MP-SP}{MP}×100=10 \)
\(\ ⇨ \frac{MP-1260}{MP}×100=10 \)
\(\ ⇨ MP-1260=\frac{10}{100}×MP \)
\(\ ⇨ MP-\frac{MP}{10}=1260 \)
\(\ ⇨ \frac{10MP-MP}{10}=1260\)
\(\ ⇨ 9MP = 12600 \)
\(\ ⇨ MP = 1400 \)
⸫ The required Marked price was Rs. 1400
6. The marked price on a watch is Rs. 1150. On account of Puja, if it is to be sold at Rs. 1000 then what will be the rate of discount?
Solution:
Given, MP = Rs. 1150
SP = Rs. 1000
We have,
Percentage of discount \(\ = \frac{MP-SP}{MP}×100 \)
\(\ = \frac{1150-1000}{1150}×100 \)%
\(\ = \frac{150}{1150}×100 \)%
\(\ = 13.043 \)%
7. A cloth seller advertises a discount of 10% and sells his clothes accordingly. A customer buys a pair of suit for Rs. 6050, shirt for Rs. 575 and a saree for Rs. 875. Calculate the total discount she got.
Solution:
Here, total SP = Rs. (6050+575+875) = Rs. 7500
Now, 10% of Rs. 7500 \(\ = \frac{10}{100}×7500 \)
\(\ = 10×75 \)
\(\ = 750 \)
⸫ The customer got a total discount of Rs. 750
8. What is the rate of retail discount on a book priced at Rs. 200 and sold at Rs. 175
Solution:
Given, MP = Rs. 200
SP = Rs. 175
We have,
Percentage of discount \(\ = \frac{MP-SP}{MP}×100 \)%
\(\ = \frac{200-175}{200}×100 \)%
\(\ = \frac{25}{2} \)%
\(\ = 12.5 \)%
9. Buying a table for Rs. 2750 from a furnisher shop, a customer gets a discount \(\ 8\frac{1}{3} \)% What was the price of the tablefixed by the shopkeeper?
Solution:
Given, SP = Rs. 2750
Let the marked price be \(\ x \)
Discount percentage = \(\ 8\frac{1}{3} = \frac{25}{3} \)
\(\ ⇨ \frac{x-2750}{x}×100= \frac{25}{3} \)
\(\ ⇨ x-2750= \frac{25}{3×100}×x \)
\(\ ⇨ x-\frac{25}{300}x= 2750 \)
\(\ ⇨ \frac{300x-25x}{300}= 2750 \)
\(\ ⇨ 275x = 825000 \)
\(\ ⇨ x = 3000 \)
⸫ The required Marked price was Rs. 3000
10. A shopkeeper gave a discount of 30% to a shirt with marked price of Rs. 600. He further gave a discount of 20% on that shirt. At what price did the shopkeeper sell the shirt and what is the total percentage of discount?
Solution:
Given, MP = Rs. 600
Discount percentage = 30
\(\ ⇨ \frac{600-SP}{600}×100=30 \)
\(\ ⇨ 600-SP=\frac{30×600}{100} \)
\(\ ⇨ SP = 600-180\)
\(\ ⇨ SP = 420 \) (Rs.)
Now, for the 2nd discound, MP = Rs. 420
Ans, Discount percentage = 20
\(\ ⇨ \frac{420-SP}{420}×100=20 \)
\(\ ⇨ 420-SP=\frac{20×420}{100} \)
\(\ ⇨ SP = 420-84\)
\(\ ⇨ SP = 336 \) (Rs.)
When SP = Rs. 336, MP = Rs. 600
⸫ Total percentage of discount \(\ = \frac{600-336}{600}×100 \)%
\(\ = \frac{264}{6} \)%
\(\ = 44 \)%
11. Kamal bought a car for Rs. 400000 and spent Rs. 10000 on repairing. He sold the car to Suresh at 10% profit and Suresh again sold it to Deepak at 5% profit. At what price Deepak bought the car?
Solution:
For Kamal,
CP = Rs. 400000
OE = Rs. 10000
⸫ Actual CP = RS. (400000+10000) = Rs. 410000
Profit made while selling to Suresh = 10% of Actual CP
\(\ = \frac{10}{100}×410000 = 41000 \)
Now, CP for Suresh = Rs. (410000+41000) = Rs. 451000
Profit made by Suresh while selling to Deepak = 5% of CP
\(\ = \frac{5}{100}×451000 = 22550 \)
So, SP for Suresh = CP for Deepak
= Rs. (451000+22550) = Rs. 473550
⸫ Deepak bought the car at Rs. 473550
12. A shopkeeper bought a radio from a man at Rs. 800. He spent Rs. 200 on repairing and sold it to another person at Rs. 1300. What was his percentage of profit?
Solution:
Here, CP = Rs. 800
OE = Rs. 200
⸫ Actual CP = RS. (800+200) = Rs. 1000
Also given SP = Rs. 1300
⸫ Percentage of profit \(\ = \frac{SP-Actual~ CP}{Actual~ CP}×100 \)%
\(\ = \frac{1300-1000}{1000}×100 \)%
\(\ = \frac{300}{1000}×100 \)%
\(\ = 30 \)%
13. Migam bought an iron for Rs. 1200. He spent Rs. 40 for transportation. At what price he should sell it to get a profit of 25%
Solution:
Here, CP = Rs. 1200
OE = Rs. 40
⸫ Actual CP = RS. (1200+40) = Rs. 1240
Also given,
percentage of profit, p = 25 %
We have,
\(\ SP = \left(\frac{100+p}{100}\right)× Actual~ CP \)
\(\ ⇨ SP = \left(\frac{100+25}{100}\right)× 1240 \)
\(\ ⇨ SP = \left(\frac{125}{100}\right)× 1240 \)
\(\ ⇨ SP = 12.5× 124 \)
\(\ ⇨ SP = 1550 \) (Rs.)
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