8th Maths : Chapter 4 : Life Mathematics : Exercise 4.2 : Profit, Loss, Discount, Overhead Expenses and GST : Text Book Back Exercises Questions with Answers, Solution

**Exercise
4.2**

** **

**1. Fill in the blanks:**

(i) Loss
or gain percentage is always calculated on the__________. **[Answer: Cost price]**

(ii) A mobile phone is sold for ₹8400
at a gain of 20%. The cost price of the mobile phone is________. **[Answer: ₹ 7000]**

**Solution:**

Let cost price of mobile be ₹ *x *

Given that selling price is ₹ 8400 and gain is 20%

As per formula,

SP = [ (100 + gain %) / 100 ] × CP

∴ by substituting we get,

8400 = [ (100 + 20) / 100 ] × *x*

8400 = [120 / 100] *x*

* x* = [8400 × 100] / 120 = ₹
**7000**

(iii) An article is sold for ₹555 at
a loss of 7 1/2 %. The cost price of the article is ________. **[Answer: ₹ 600 ]**

**Solution:**

Given selling price is
₹ 555 & loss is 7 1/2%

as per formula,

SP = [ (100−loss %) / 100 ] × CP

by substituting, we get

555 = [ (100 – 7 1/2) / 100 ] × CP

∴ 555 = [ (100 – 15/2) /100 ] × CP = [ ( (200 – 15)/2) / 100 ] × CP

555 = [ (185/2) / 100 ] × CP

∴ CP = (555 × 100) / (185/2)
= [ (555 × 100) / 185 ] × 2 = ₹ **600**

(iv) A mixer grinder marked at ₹4500
is sold for ₹4140 after discount. The rate of discount is __________. **[Answer: 8%]**

**Solution:**

Marked price is ₹ 4500

Discounted price in ₹ 4140

∴ Discount = Marked price − Discounted price

= 4500 − 4140 = 360

∴ Rate of discount = [ **Discount
/ Marked Price ]** × 100

= [360 / 4500] × 100 = **8%**

(v) The total bill amount of a shirt
costing ₹575 and a T-shirt costing ₹325 with GST of 5% is_______. **[Answer: ₹ 945]**

**Solution:**

Cost price of shirt = ₹ 575 (CP)

GST = 5%

Bill amount formula = CP × [ (100 + GST%) / 100]

= 575 × [(100 + 5) / 100] = 575 × [105 / 100] = ₹ 603.75

Cost price of T−shirt = ₹ 325 (CP)

GST = 5%

Bill amount = CP × [ (100 + GST%) / 100]

= 325 × [ (100 + 5) / 100 ] =
₹ 341.25

∴ Total bill amount = ₹ 603.75 + ₹ 341.25 = **₹ 945**

** **

**2. If selling an article for ₹820 causes
10% loss on the selling price, then find its cost price.**

**Solution 1:**

Solution 2:

Given that selling price (SP) = ₹ 820

Loss % = 10%

As per formula SP = CP × [ (100 – loss%) / 100 ]

∴ Substituting in formula, we get

820 = CP × [ (100 – 10) / 100]

∴ CP = [ 820 × 100 ] / 90 = **911**

** **

**3. If the profit earned on selling an
article for ₹810 is the same as loss on selling it for ₹530, then find the cost
price of the article.**

**Solution:**

Case 1: Profit = Selling price (SP) − Cost price (CP)

Case 2: Loss = Cost price (CP) − Selling price (SP)

Given that profit of case 1 = loss of case 2

∴ P = 810 − CP

L = CP − 530

Since profit (P) = loss (L)

810 − CP = CP − 530

∴ 2CP = 810 + 530 =
1340 ⇒ C.P = 1340/2

∴ CP = **670**

** **

**4. If the selling price of 10 rulers
is the same as the cost price of 15 rulers, then find the profit percentage.**

**Solution:**

Let cost price of one ruler be *x*

Given that selling price (SP) of 10 rulers,

i.e., same as cost price (CP) of 15 rulers

∴ SP of 10 rulers =
15 × *x* = 15*x*

∴ SP of 1 ruler = 15*x* / 10 = 1.5*x*

∴ Gain = SP of 1 ruler − CP of 1 ruler = 1.5*x* − *x* =
0.5*x*

Gain % = [ Gain / CP ] × 100 = [ 0.5*x* / *x* ] × 100
= **50%**

** **

**5. Some articles are bought at 2 for
₹15 and sold at 3 for ₹25. Find the gain percentage.**

**Solution:**

Let cost price of one article be C.P

Given that 2 are bought for
₹ 15

∴ 2 × CP = 15 ⇒ CP= 15/2

Let selling price of one article be SP

Given that 3 are sold for ₹ 25

∴ 3 × SP = 25 ⇒ SP = 25/3

∴ Gain = SP – CP = 25/3 – 15/2 = [50 – 45] / 6 = 5/6

Gain % = [Gain / CP] × 100 = [ (5/6) / (15/2) ] × 100 = [ 5/6 ×
2/15 ] × 100 = 100/9

= 11 1/9 %

** **

**6. By selling a speaker for ₹768, a man
loses 20%. In order to gain 20%, how much should he sell the speaker?**

**Solution 1:**

Solution 2:

Selling price (SP) of speaker = ₹ 768

Loss % = 20%

as per formula

SP = CP × [ (100 − loss %) / 100 ]

∴ 768 = CP × [ (100 – 20) /100 ]

∴ CP = [ 768 × 100 ] / 80 = 960

For gain of 20%, we should now calculate the selling price

∴ SP = CP [ (100 + gain%) / 100]

= 960 [ (100 + 20) /100 ] = 960 × (120 / 100)

= 96 × 12 **= ₹ 1152**

** **

**7. Find the unknowns x, y
and z.**

**Solution 1:**

Solution 2:

**(i)** Book marked price = ₹225 discount =
8%

∴ Selling price (*x*)
= Marked price × [ (100 – *d*%) / 100 ]

= 225 × [ (100 – 8) / 100] = 225 × [92 / 100] = **₹ 207**

**(ii)** LED TV selling price = 11970 discount
= 5%, Marked price = *y*

∴ Selling price = Marked price *y* × [(100 – *d*%) / 100]

∴ 11970 = *y* × [ (100 – 5) / 100 ]

∴ *y* = [11970 × 100] / 95 = 126 × 100 = **₹ 12,600**

**(iii)** Digital clock marked price (MP) = ₹
750, MP = ₹ 12,600

Selling price (SP) = ₹ 615, Discount = *z*

SP = MP × [ (100 – *d*%) / 100 ]

∴ 615 = 750 × [ (100 – *z*) / 100 ]

∴ (100 − *z*) = [615
× 100] / 750

∴ 100 – *z* = 82

∴ z = 100 − 82, **Discount
= 18%**

** **

**8. Find the total bill amount for the
data given below:**

**Solution 1:**

Solution 2:

Formula for discounted price DP = Marked price (MP) × [ (100 – *d*%) / 100 ]

When d is the discount %

∴ DP = MP × [(100 – *d*%) / 100]

(i) School bag = MP × [(100 – *d*%) / 100]

= 500 × [ (100 – 5) / 100 ] = [500 × 0.95] / 100 = ₹ 475

(ii) Hair drier = MP × [ (100 – *d*%) / 100 ]

= 2000 × [(100 – 10) / 100] = 2000 × 0.9 = ₹ 1,800

For bill amount, we should apply GST on the discounted value of
the items.

Formula: Bill amount = Discounted price × [ (l00 + GST%) / 100 ]

∴ For (i) School bag,

Bill amount = 475 × [ (100
+ 12) / 100 ] = 475 × 1.12 = **₹ 532**

∴ For (ii) Hair
drier,

Bill amount = 1800 × [ (100 + 28) / 100 ] = 1800 × 1.28 = **₹
2,304**

∴ Total bill amount =
Bill amount of School bag + Stationary + Cosmetics + Hair drier

= 532 + 2304

= **₹ 2,836**

** **

**9. A branded Air-Conditioner (AC) has
a marked price of ₹38000. There are 2 options given for the customer.**

**(i) Selling Price is the same ₹38000
but with attractive gifts worth ₹3000**

**(or)**

**(ii) Discount of 8% on the marked price
but no free gifts. Which offer is better?**

**Solution:**

Marked price of AC = ₹ 38,000

Option 1:

Selling price = ₹ 38000 & gifts worth ₹ 3000

Net gain for customer = ₹ 3000 as there is no discount on AC

Option 2:

Discount of 8%, but no gift

∴ Discounted value = MP × [ (l00 − *d*%) / 100 ]

= 38000 × [ (100 – 8) / 100 ] = 38000 × 0.92 = 34960

Savings for customer = 38000 – 34960 = ₹ 3040

Therefore, the customer gets 3000 gift in option 1 where as he
is able to save only ₹ 3040 in option 2. Therefore, option 2 is better.

** **

**10. If a mattress is marked for ₹7500
and is available at two successive discounts of 10% and 20%, find the amount to
be paid by the customer.**

**Solution:**

Solution 2:

Marked price of mattress = ₹
7500

Discount *d*_{1}
= 10%

Discount *d*_{2}
= 20%

Price after discount *d*_{1
} = MP × [ (100 − *d*_{1}%)
/ 100 ]

= 7500 × [ (100 − 10) / 100 ] =
7500 × 90/100 = 6750

Price after second discount *d*_{2 }= Discount price × [ (100 − *d*_{2
}%) / 100 ]

= 6750 × [ (100 − 20) / 100 ]
= ₹** 5400**

** **

**Objective
Type Questions**

**11. A fruit vendor sells fruits for ₹200
gaining ₹40. His gain percentage is**

(A)20%

(B) 22%

(C) 25%

(D) 16 2/3
%

**[Answer: (C) 25%]**

**Solution:**

Selling price = ₹ 200

Gain = 40

∴ CP = Selling price − gain = 200 – 40 = 160

Gain % = [**Gain / CP] **× 100 = [40 / 160] × 100 = **25%**

**12. By selling a flower pot for ₹528,
a woman gains 20%. At what price should she sell it to gain 25%?**

(A) ₹500

(B) ₹550

(C) ₹553

(D) ₹573

**[Answer: (B) ₹ 550]**

**Solution:**

Solution 2:

If selling price (SP) = ₹
528

Gain % = 20%

∴ CP = ?

Selling price SP = CP × [ (100
+ gain %) / 100 ]

∴ 528 = CP × [ (100 + 20) / 100 ]

∴ CP = [528 × 100] / 120 = 440

If gain % = 25%, Selling
price?

Selling price SP = CP × [ (100
+ gain%) / 100 ]

= 440 × [ (100 + 25) / 100 ] =
440 × [125 / 100] = **₹ 550**

**13. A man buys an article for ₹150 and
makes overhead expenses which are 12% of the cost price. At what price must he sell
it to gain 5%?**

(A) ₹180

(B) ₹168

(C) ₹176.40

(D) ₹88.20

**[Answer:** **(C) 176.40]**

**Solution:**

Cost price of article = ₹ 150

Over head expenses = 12% of cost price

= (12 / 100) × 150 = ₹ 18

∴ Effective cost of article = 150 + 18 = ₹ 168

Now, to gain 5%, he has to sell at

SP = CP × [ (100 + gain%) / 100]

= 168 × [ (100 + 5) / 100] = 168 × 1.05 = **176.40**

**14. What is the marked price of a hat
which is bought for ₹210 at 16% discount?**

(A) ₹243

(B) ₹176

(C) ₹230

(D) ₹250

**[Answer: (D) ₹ 250]**

**Solution:**

Solution 2:

Let marked price be MP

Discounted price = ₹ 210

Rate of discount = 16%

As per formula :

Discounted price = MP × [ (100 – *d*%) / 100 ] = (100 – 16) / 100

MP = [210 × 100] / 84 = **250**

**15. The single discount in % which is
equivalent to two successive discounts of 20% and 25% is**

(A) 40%

(B) 45%

(C) 5%

(D) 22.5%

**[Answer: (A) 40%]**

**Solution:**

Solution 2:

Let marked price be MP, after discount 1 of 20%,

Discounted price = MP × [ (100 – *d*_{1}%) / 100 ]
= [100 – 20] / 100 = MP × [80/100]

After discount 2 of 25%,

Discounted price = Discounted price × [ (100 – *d*_{2}%)
/ 100 ]

= MP × 80/100 × [ (100 – 25) / 100 ]

= MP × [ (80 × 75) / (100
× 100) ] = MP × (60 / 100)

= MP × [ (100 – 40) / 100 ] 60 can be written
as 100 − 40

Comparing with formula, we get

∴ This is equivalent to a
single discount of **40%**

**Answer:**

**Exercise 4.2 **

**1. (i) Cost price (ii)
₹7000 (iii) ₹600 (iv) 8% (v) ₹945 **

**2. ₹902 **

**3. ₹670 **

**4. 50% **

**5. 11 (1/9) % **

**6. ₹1152 **

**7. (i) x = ₹207 (ii) y = ₹12600 (iii) z = 18%
**

**8. ₹2836 **

**9. Discount of 8% is
better **

**10. ₹5400 **

**11. (C) 25% **

**12. (B) 550 **

**13. (B) 168 **

**14. (D) ₹250 **

**15. (A) 40%**

** **

Tags : Questions with Answers, Solution | Life Mathematics | Chapter 4 | 8th Maths , 8th Maths : Chapter 4 : Life Mathematics

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8th Maths : Chapter 4 : Life Mathematics : Exercise 4.2 (Profit, Loss, Discount, Expenses and GST) | Questions with Answers, Solution | Life Mathematics | Chapter 4 | 8th Maths

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