Exercise 8.2 | Class 8 | SCERT Solution | General Mathematics

1. The marked price of a radio is Rs. 2055. If it is sold at 3% discount, find the selling price.
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.)