Exercise 2.2


Important Formulae:
$SP = MP( 1 - \frac{d%}{100})$

Solutions

General Section


4 a) The marked price of a mobile is Rs 12 600 and 10% discount is allowed.
(i) Find the discount amount.
(ii) Find the selling price of the mobile.
(iii) How much is its price with 13% VAT?

Solution:
Here,
MP = $Rs 12 600$
Discount percentage (d%) = $10\%$

(i) discount amount = $d\% of MP = 10% of 12600$

$= Rs 1 260$
(ii) selling price = $MP - discount$

$= 12 600 - 1260$
$= Rs 11340$
(iii) Selling price with 13% VAT = $SP ( 1 + \frac{13}{100} )$

$= 11340 * \dfrac{113}{100}$
$= Rs 12814.20$

Creative Section - A


5 a) The marked price of a lady bag is Rs 4 800. If a customer is given 10 % discount, how much does he/she pay with 15% VAT?

Solution:

For a lady bag,
Marked Price (MP) = Rs 4800
Discount percentage (d%) = 10%
VAT percentage (VAT%) = 15%
To find: Selling Price with VAT (SP with VAT) = ?


We know,
SP = $MP ( 1 - \frac{d%}{100})$

Also,
SP with VAT = $SP(1 + \frac{VAT%}{100}$


From above two formulae, we get,

SP with VAT = $MP(1 - \frac{d%}{100})(1 + \frac{VAT%}{100}$

$= MP ( 1 - \frac{10}{100})(1 + \frac{15}{100})$

$= MP × \dfrac{100-10}{100} × \dfrac{100+15}{100}$

$= 4800 × \dfrac{90}{100} × \dfrac{113}{100}$

$= \dfrac{48 × 9 × 115}{10}$

$= Rs 4968$
Hence, the required selling price of the lady bag including VAT after discount is Rs 4968.


6 a) The marked price of a woolen sweater is Rs 1 750. If the shopkeeper allows 20% discount and makes a profit of Rs 150, at what price did he purchase the sweater?

Solution:

For a woolen sweater,
Marked Price (MP) = Rs 1750
Discount percentage (d%) = 20%
Profit amount (P) = Rs 150

To find: Cost Price (CP) = ?


We know,
Selling Price = $MP( 1 - \frac{d%}{100})$

$= MP ( 1 - \frac{20}{100})$

$= 1750 × \dfrac{80}{100}$

$= Rs 1400$


Now,

Cost Price = SP - P

$or, CP = 1400 - 150$

$\therefore CP = Rs 1250$

Hence, the required cost price of the woolen seater is Rs 1250.


6 c) Mr. Rai bought a radio for Rs 2 000 and fixed its price so that after giving 20 % discount he made 10 % profit. Find the fixed price of the radio.

Solution:

For a radio,
Cost Price (CP) = Rs 2000
Discount percentage (d%) = 20%
Profit Percentage (P%) = 10%

We know,
The fixed price is the marked price.

And,
Selling Price = $CP(1 + \frac{P%}{100})$
Selling Price = $MP(1 - \frac{d%}{100})$


From above two formulae, we get,
$CP ( 1 + \frac{P%}{100} = MP(1 - \frac{d%}{100})$

$or, 2000 ( 1 + \frac{10}{100}) = MP ( 1 - \frac{20}{100}$

$or, 2000 × \dfrac{110}{100} = MP × \dfrac{80}{100}$

$or, 2200 = MP × \dfrac{80}{100}$

$or, MP = 2200 × \dfrac{100}{80}$

$\therefore MP = Rs 1760$

Hence, the required fixed price of the radio is Rs 1760.
6 e) The marked price of an article is Rs 2 800 which is 40% above the cost price. If it is sold by allowing 20% discount, what  will be the profit percent?

Solution:

For an article,
Marked Price (MP) = Rs 2800

Marked Price (MP) = CP + 40% of CP

$or, 2800 = CP ( 1 + 40%)$

$or, 2800 = CP ( 1 + \frac{40}{100})$

$or, 2800 = CP × \frac{140}{100}$

$or, CP = \dfrac{2800×100}{140}$

$\therefore CP = Rs 2000$


And,
Selling price (SP) = $MP (1 - \frac{d%}{100}$

$= MP ( 1 - \frac{20}{100})$

$= 2800 × \frac{80}{100}$

$= Rs 2240$


Now,
Profit percentage (P%) = $\dfrac{SP - CP}{CP} × 100%$

$= \dfrac{2240 - 2000}{2000} × 100%$

$= \dfrac{240}{2000} × 100%$

$= 12%$

Hence, the required profit percentage in the trade of the article is 12%.


7 a) A trader marks the price of his/her good 40% above the cost price and allows 20% discount. If his/her purchase price of an item is Rs 6 000, how much should a customer pay for it levying 13% VAT?

Solution:

Given,
Cost price (CP) = Rs 6000



Marked Price (MP) = $CP(1 + 40%)$

$= CP ( 1 + \frac{40}{100})$

$= 6000 × \frac{140}{100}$

$= Rs 8400$



Discount percentage (d%) = 20%

Now,
Selling Price (SP) = $MP ( 1 - \frac{d%}{100})$

$= MP ( 1 - \frac{20}{100})$

$= 8400 × \frac{80}{100}$

$= Rs 6720$


And,
VAT percentage (VAT%) = 13%
SP with VAT = $SP ( 1 + \frac{VAT%}{100})$

$= SP ( 1 + \frac{13}{100})$

$= 6720 × \frac{113}{100}$

$= Rs 7593.60$

Hence, a customer should pay Rs 7593.60 with 13% VAT.


7 c) The marked price of an article is Rs 4 500. After allowing some percent of discount and levying 10% VAT it is sold at Rs 4 400, find the discount percent.

Solution:

For an article,
Marked Price (MP) = Rs 4500
VAT percent (VAT%) = 10%
SP with VAT = Rs 4400
Discount percent = d%

We know,

SP = $\dfrac{SP with VAT}{100 + \frac{VAT%}{100}}$

$= \dfrac{4400}{100 + \frac{10}{100}}$

$= \dfrac{4400}{\frac{110}{100}}$

$= 4400 × \frac{100}{110}$

$= Rs 4000$

And,
d% = $\dfrac{MP - SP}{MP} × 100%$

$= \dfrac{4500 - 4000}{4500} × 100%

$= 11.11%$

Hence, the required discount percentage in the marked price is 11.11%.


8 a) A grocer fixed the price of his goods 25% above the cost price. If he/she sold a box of noodles allowing 5% discount, find his profit percent.

Solution:

Let the Cost Price be represented by CP.

Here,
Marked Price = $CP ( 1+ \frac{25}{100})$

$= CP  × \frac{125}{100}$

$= \frac{5CP}{4}$


And,
When discount percentage (d%) = 5%,

SP = MP ( 1 - $\frac{d%}{100}$)

$= \frac{5CP}{4} × (1 - \frac{5}{100})$

$= \frac{5CP}{4} × \frac{95}{100}$

$= \frac{95CP}{80}$


Now,
Profit percentage = $\dfrac{SP -CP}{CP} × 100%$

$= \dfrac{ \frac{95 CP}{80} - CP}{CP} × 100%$

$= \dfrac{ \frac{95 CP - 80 CP}{80}}{CP} × 100%$

$= \dfrac{15CP}{80} × \dfrac{1}{CP} × 100%$

$= \dfrac{15}{80} × 100%$

$= 18.75%$

Hence, the required profit percentage in the given transaction is 18.75%.




Creative Section - A

5 a) 

6 a) 

6 c) 

6 e) 

7 a) 

7 c) 

8 a) 

8 d) A trader fixed the price of cosmetic items 30% above the cost price. When he/she sold an item at 25% discount, there was a loss of Rs 15. Find the cost price and marked price of the item.

8 g) Mrs. Sharma fixed the price of a pen to make a profit of 10%. But she sold it allowing a discount of Rs 7.50 and lost 5%. At what price did she purchase the pen?

9 a) 

10 a) 

11 a) A shopkeeper purchased a bicycle for Rs 5000 and marked its price a certain percent above the cost price. Then, he sold it at 10% discount. If a customer paid Rs 6356.25 with 13% VAT to buy it, how many percent is marked price above the cost price? 

12 a) When an article was sold at a discount of 10%, a customer paid Rs 9,153 with 13% VAT. If 8% profit was made in this transaction by how many percent was the marked price above the cost price? 

13 a) After allowing 25% discount on the marked price and then levying 10% VAT, a cycle was sold. If the discount amount was Rs 750, how much VAT  was levied on the price of the cycle? 


About vedanta EXCEL in MATHEMATICS Book 10

Author: Hukum Pd. Dahal
Editor: Tara Bahadur Magar

Vanasthali, Kathmandu, Nepal
+977-10-4382404, 01-4362082
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Class 10 - Marked Price, Discount and Value Added Tax - Tax and Money Exchange - Solved Exercises | vedanta Excel in Mathematics is a collection of the solutions related to exercises of MP, Discount and VAT from Tax and Money Exchange Chapter for Nepal's Secondary Education Examination (SEE) appearing students.

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