# DAV Class 8 Maths Chapter 5 Brain Teasers Solutions

The DAV Class 8 Maths Book Solutions Pdf and DAV Class 8 Maths Chapter 5 Brain Teasers Solutions of Compound Interest offer comprehensive answers to textbook questions.

## DAV Class 8 Maths Ch 5 Brain Teasers Solutions

Question 1A.
Tick (✓) the correct option.

(i) If the selling price of an article is twice the cost price, the profit percent is _______
(a) 50%
(b) 100%
(c) 150%
(d) 200%
Solution:
(b) 100%
Let the C.P. of the article be x.
Then, S.P. = 2x.
∴ Profit = S.P. – C.P.
= 2x – x = x
Profit % = $$\frac{\text { Profit }}{\text { C.P. }}$$ × 100
= $$\frac{x}{x}$$ × 100
= 100%

(ii) A jeans is marked for ₹ 2,590, but is sold for ₹ 2,331, then discount % is _______
(a) 20%
(b) 15%
(c) 10%
(d) 5%
Solution:
(c) 10%
M.P. = ₹ 2,590
S.P. = ₹ 2331
Discount = M.P. – S.P.
= ₹ 2,590 – ₹ 2331 = ₹ 259
Discount % = $$\frac{\text { Discount }}{\text { M.P. }}$$ × 100
= $$\frac{259}{2590}$$ × 100 = 10 %

(iii) If selling price of five pens is equal to the cost price of four pens, then the gain or loss% is _______
(a) 20% gain
(b) 20% loss
(c) 25% loss
(d) 25% gain
Solution:
(b) 20% loss
Let the C.P. of 1 pen be x.
So the C.P. of 4 pens = 4x
and C.P. of 5 pens = 5x.
S.P. of 5 pens = 4x
Loss = C.P. – S.P.
= 5x – 4x = x
∴ Loss% = $$\frac{\text { Loss }}{\mathrm{CP}}$$ × 100
= $$\frac{x}{5 x}$$ × 100 = 20%.

(iv) Selling price of a saree is ₹ 864 including 8% VAT. The original price of the saree is
(a) ₹ 842
(b) ₹ 800
(c) ₹ 801.50
(d) ₹ 820
Solution:
(b) ₹ 800
Let the original price of the saree be x.
So, x + 8% of x = 864
⇒ x + $$\frac{8}{100}$$ × x = 864
⇒ $$\frac{100 x+8 x}{100}$$ = 864
⇒ $$\frac{108 x}{100}$$ = 864
∴ x = $$\frac{864 \times 100}{108}$$ = ₹ 800.
Thus, the original price of the saree = ₹ 800.

(v) Discount is always calculated on _______
(a) cost price
(b) marked price
(c) selling price
(d) VAT
Solution:
(b) marked price

Question 1B.
(i) After giving a discount of 8% on the marked price, an article was sold for ₹ 414. Find the marked price of the article.
(ii) A fan is sold for ₹ 650. The gain is one-fourth of the cost price of the fan. Find the gain per cent.
(iii) A shopkeeper buys pencils at 10 for ₹ 10 and sells them at 8 for ₹ 10. Find the profit per cent.
(iv) Find the rate of VAT if an article marked at ₹ 5,000 is sold for ₹ 5,200?
(v) A person pays ₹ 2,800 for a cooler marked at ₹ 3,500. Find the discount per cent offered.
Solution:
(i) Discount = 8%
S.P. = ₹ 144
M.P. = ?
∵ M.P. = $$\frac{\text { S.P. } \times 100}{100-\text { Discount } \%}$$
= $$\frac{414 \times 100}{100-8}$$
= $$\frac{414 \times 100}{92}$$
= ₹ 450.

(ii) S.P. = ₹ 650
Let C.P. of the fan be x.
So, gain = $$\frac{1}{4}$$ x
Now, gain = S.P. – C.P.
⇒ $$\frac{x}{4}$$ = 650 – x
⇒ x + $$\frac{x}{4}$$ = 650
⇒ $$\frac{5 x}{4}$$ = 650
⇒ x = $$\frac{650 \times 4}{5}$$ = ₹ 520
Thus, gain = $$\frac{1}{4}$$ × 520 = ₹ 130.
Gain % = $$\frac{\text { Gain } \times 100}{\text { C.P. }}$$
= $$\frac{130 \times 100}{520}$$ = 25%

(iii) C.P. of 10 pencils = ₹ 10
= C.P. of 8 pencils = ₹ 8
And, SP. of 8 pencils = ₹ 10.
Gain = S.P. – C.P.
= 10 – 8 = ₹ 2.
Gain % = $$\frac{\text { Gain }}{\text { C.P. }}$$ × 100
= $$\frac{2}{8}$$ × 100 = 25%

(iv) MP. = ₹ 5000
S.P. = ₹ 5200
VAT = S.P. – MP.
= ₹ 5000 – ₹ 5200 = ₹ 200
Rate of VAT = $$\frac{200}{5000}$$ × 100 = 4%.

(v) M.P. = ₹ 3500
S.P. =₹ 2800
Discount = M.P. – S.P.
= 3500 – 2800 = ₹ 700
Discount % = $$\frac{\text { Discount }}{\text { M.P. }}$$ × 100
= $$\frac{700}{3500}$$ × 100 = 20%

Question 2.
Rajan purchased a purse at 25% discount on its marked price but sold it at the marked price. Find the gain per cent of Rajan on his transaction.
Solution:
Let the marked price be ₹ x.
Discount = $$\frac{25}{100}$$ × x
= ₹ $$\frac{x}{4}$$
C.P. of the purse = x – $$\frac{x}{4}$$
= ₹ $$\frac{3 x}{4}$$
S.P. = M.P. = ₹ x
Gain = S.P. – C.P.
= x – $$\frac{3 x}{4}$$
= ₹ $$\frac{x}{4}$$

Gain % = $$\frac{\text { Gain }}{\text { C.P. }}$$ × 100
= $$\frac{\frac{x}{4}}{\frac{3 x}{4}}$$ × 100
= $$\frac{100}{3}$$
= 33$$\frac{1}{3}$$
Hence, the gain on the transaction = 33$$\frac{1}{3}$$ %.

Question 3.
Jasleen marks her goods at 30% above the cost price and allows a discount of 25% on the marked price. Find her gain or loss per cent.
Solution:
Let the C.P. be ₹ x
∴ Marked price = x + $$\frac{30}{100}$$
= ₹ $$\frac{13}{10}$$ x

Discount = M.P. × $$\frac{25}{100}$$
= $$\frac{13 x}{10} \times \frac{25}{100}$$
= ₹ $$\frac{13 x}{40}$$

∴ S.P. = M.P. – Discount
= $$₹ \frac{13 x}{10}-₹ \frac{13 x}{40}$$
= ₹ $$\frac{39 x}{40}$$

Here C.P. > S.P.
Loss = C.P. – S.P.
= ₹ x – ₹ $$\frac{39 x}{40}$$
= ₹ $$\frac{x}{40}$$

Loss % = $$\frac{\text { Loss }}{\text { C.P. }}$$ × 100
= $$\frac{\frac{x}{40}}{x}$$ × 100
= $$\frac{5}{2}$$%
= $$2 \frac{1}{2}$$%
Hence, the loss % = 2 $$\frac{1}{2}$$%.

Question 4.
How much per cent above the cost price should a shopkeeper mark his goods so that after allowing a discount of 20% on the marked price, he gains 12%?
Solution:
Let the M.P. be ₹ x.
Discount = $$\frac{20}{100}$$ × x
= ₹ $$\frac{x}{5}$$
∴ Selling price = M.P. – Discount
= x – $$\frac{x}{5}$$
= ₹ $$\frac{4 x}{5}$$

Now S.P. = C.P. (1 + $$\frac{\text { Gain }}{100}$$)
$$\frac{4 x}{5}=\text { C.P. }\left(1+\frac{12}{100}\right)$$
⇒ $$\frac{4 x}{5}=\text { C.P. } \times \frac{28}{25}$$
⇒ C.P. = $$\frac{4 x}{5} \times \frac{25}{28}$$
= ₹ $$\frac{5 x}{7}$$

Difference between M.P. and C.P. = x – $$\frac{5 x}{7}$$
= ₹ $$\frac{2 x}{7}$$
∴ Percentage of difference = $$\frac{\frac{2 x}{7}}{\frac{5 x}{7}}$$ × 100 = 40%
Hence, the shopkeeper should mark his good above 40% of his C.P.

Question 5.
Rohit marks his goods at 40% above the cost price but allows a discount of 5% for cash payment to his customers. What actual profit does he make, if he receives ₹ 1064 after allowing the discount?
Solution:
Let C.P. be ₹ x.
∴ M.P. = ₹ x + $$\frac{40 x}{100}$$
= ₹ $$\frac{7 x}{5}$$

Discount = $$\frac{7 x}{5} \times \frac{5}{100}$$
= ₹ $$\frac{7 x}{100}$$

∴ S.P. = M.P. – Discount
= ₹ $$\frac{7 x}{5}-\frac{7 x}{100}$$
= ₹ $$\frac{7 x}{100}$$

Now $$\frac{133}{100}$$ x = 1064
x = 1064 × $$\frac{100}{133}$$
⇒ x = 8 × 100 = 80

∴ C.P. = ₹ 800
and S.P. = 1064
Profit = S.P. – C.P.
= ₹ 1064 – ₹ 800 = ₹ 264
Hence, the actual profit is ₹ 264.

Question 6.
Mr. Kumar went to shopping with his family to a Mall. Mrs. Kumar bought a saree for ₹ 12500, cloths for the kids for ₹ 9280 and a mobile for Mr. Kumar for ₹ 32638. If the VAT charged on their purchases is 7.5% , then what is the total amount that Mr. Kumar has paid?
Solution:
Cost price for a saree = ₹ 12,500
VAT = $$\frac{7.5}{100}$$ × 12500
= ₹ 937.50
∴ Total cost including VAT = ₹ 12500 + ₹ 937.50 = ₹ 13437.50

Cost price for cloths for kids = ₹ 9,280
VAT = $$\frac{7.5}{100}$$ × 9280
= ₹ 696
∴ Total cost including VAT = ₹ 9280 + ₹ 696 =₹ 9976

Cost of mobile for Mr. Kumar = ₹ 32638
VAT = $$\frac{7.5}{100}$$ × 32638
= ₹ 2447.85 100
Total cost including VAT = ₹ 32638 + ₹ 2447.85 = ₹ 35085.85

∴ Total cost of all items including VAT paid by Mr. Kumar = ₹ 13437.50 + ₹ 9976 + ₹ 35085.85 = ₹ 58499.35.

### DAV Class 8 Maths Chapter 5 HOTS

Question 1.
The marked price of an article is ₹ 3,500 and rate of VAT is 8%. A shopkeeper allows a discount of 20% and still makes a profit of 10%. Find the original cost price of the article and the selling price including VAT.
Solution:
M.P. = ₹ 3500
VAT = 8%
Discount = 20%
Discount = 20 %
Let C.P. be x so that
S.P. = C.P. (1 + $$\frac{\text { gain\% }}{100}$$)
= x (1 + $$\frac{10}{100}$$)
= $$\frac{11 x}{10}$$ ………………….(1)
S.P. = M.P. (1 – $$\frac{\text { Discount% }}{100}$$)
= 3500 (1 – $$\frac{20}{100}$$)
= 3500 × $$\left(\frac{100-20}{100}\right)$$
= 3500 × $$\frac{80}{100}$$
= ₹ 2800

∴ S.P. including VAT = 2800 + $$\frac{8}{100}$$ × 2800
= 2800 + 224
= ₹ 3024 ………………..(2)
From (1) and (2)
Now, $$\frac{11 x}{10}$$ = 3024
⇒ x = $$\frac{3024 \times 10}{11}$$ ~ 2749.10

Question 1.
An article is sold for ₹ 96 at a profit equal to its C.P. in rupees. Find the cost price of the article.
Solution:
Let C.P. of the article be ₹ x.
∴ ₹ Profit = x × $$\frac{x}{100}$$
= ₹ $$\frac{x^2}{100}$$
∴ x + $$\frac{x^2}{100}$$ = 96
⇒ $$\frac{x^2+100 x}{100}$$ = 96
⇒ x<sup>2</sup> + 100x = 9600
⇒ x<sup>2</sup> + 100x – 9600 = 0
⇒ x<sup></sup> + 160x – 60x – 9600 = 0
⇒ x (x + 160) – 60 (x + 160) = 0
⇒ (x + 160) (x – 60) = 0
⇒ x = 60 and x = – 160 (neglected as cost can never be negative)
Hence, the cost price of the article is ₹ 60.

Question 2.
An article is sold for ₹ 24 at a loss percent equal to its C.P. in rupees. Find the C.P. of the article.
Solution:
Let the C.P. of the article be ₹ x.
∴ Loss = x × $$\frac{x}{100}$$
= ₹ $$\frac{x^2}{100}$$
S.P. = C.P. – Loss
= x – $$\frac{x^2}{100}$$
Then, x – $$\frac{x^2}{100}$$ = 24
⇒ $$\frac{100 x-x^2}{100}$$ = 24
⇒ 100x – x2 = 2400
⇒ x2 – 100x + 2400 = 0
⇒ x2 – 60x – 40x + 2400 = 0
⇒ x (x – 60) – 40 (x – 60) = 0
⇒ (x – 60) (x – 40) = 0
⇒ x = 60 and x = 40
Hence, the cost price of the article is ₹ 60 or ₹ 40.

Question 3.
An article is sold for ₹ 3120 at a loss of 4%. What will be the gain or loss per cent, if it is sold for ₹ 3640?
Solution:
S.P. = ₹ 3120
Loss = 4%
∴ S.P. = C.P. (1 – $$\frac{\text { Loss }}{100}$$)
3120 = C.P. (1 – $$\frac{4}{100}$$)
3120 = C.P. $$\frac{24}{25}$$
C.P. = $$\frac{3120 \times 25}{24}$$
= ₹ 3250
But new S.P. = ₹ 3640
Here S.P. > C.P.
∴ Gain = S.P. – C.P.
= ₹ 3640 – ₹ 3250 = ₹ 390
∴ Gain % = $$\frac{\text { Gain }}{\text { C.P. }}$$ × 100
= $$\frac{390}{3250}$$ × 100 = 12%
Hence, the gain = 12%.

Question 4.
Find a single discount equivalent to two successive discounts of 25% and 4%.
Solution:
Let M.P. be ₹ 100.
∴ S.P. = (100 – 25)% of (100 – 4)% of 100
= $$\frac{75}{100} \times \frac{96}{100}$$ × 100 = ₹ 72
∴ Single discount is (100 – 72)% = 28%
Hence, the required single discount is 28%.

Question 5.
A shopkeeper fixed the marked price of an item 35% above its cost price. Find the discount percent so as to gain 8%.
Solution:
Let C.P. be ₹ x.
∴ M.P. = x + $$\frac{35}{100}$$ x = ₹ $$\frac{27 x}{20}$$
S.P.= C.P. + (1 + $$\frac{\text { Gain }}{100}$$)
= x (1 + $$\frac{8}{100}$$)
= ₹ $$\frac{27}{25}$$ x

Discount = M.P. – S.P.
= $$\frac{27 x}{20}-\frac{27}{25} x$$
= ₹ $$\frac{27 x}{100}$$ x%

Discount % = $$\frac{\text { Discount }}{\text { M.P. }}$$ × 100
= $$\frac{\frac{27 x}{100}}{\frac{27 x}{20}}$$ × 100 = 20 %
Hence, the required discount is 20%.

Question 6.
When a discount of 15% is allowed on the marked price of an article, it is sold for ? 2975.
(i) Calculate the marked price.
(ii) Given that the marked price is 40% above the cost price, find the cost price.
(iii) Find the gain per cent obtained on selling the article.
Solution:
(i) Discount = 15%
S.P. = ₹ 2975
Let M.P. be ₹ x.
∴ Discount = $$\frac{15}{100}$$ × x
= ₹ $$\frac{3 x}{20}$$
S.P. = M.P. – Discount
⇒ 2975 = x – $$\frac{3 x}{20}$$
⇒ 2975 = $$\frac{17 x}{20}$$
⇒ x = $$\frac{2975 \times 20}{17}$$
= ₹ 3500
Hence, M.P. = ₹ 3500

(ii) Let C.P. be ₹ x
∴ M.P. = x + $$\frac{40}{100}$$ x
⇒ 3500 = $$\frac{140}{100}$$ x
∴ x = $$\frac{3500 \times 100}{140}$$
= ₹ 2500
Hence, the cost price = ₹ 2500.

(iii) C.P. = ₹ 2500
and S.P. = ₹ 2975
∴ Gain = ₹ 2975 – ₹ 2500 = ₹ 475
Gain % = $$\frac{\text { Gain }}{\text { C.P. }}$$ × 100
= $$\frac{475}{2500}$$ × 100 = 19%
Hence, the required gain per cent = 19%.

Question 7.
A dealer purchased a washing machine for ₹ 15320. He allows a discount of 12% on its marked price and gains 10% on it. Find the marked price of the machine.
Solution:
Let M.P. be ₹ x.
∴ Discount = $$\frac{12}{100}$$ × x
= ₹ $$\frac{3 x}{25}$$
S.P. = M.P. – Discount
= x – $$\frac{3 x}{25}$$
= ₹ $$\frac{22 x}{25}$$
C.P. = ₹ 15320
Gain = 10% of ₹ 15320
= $$\frac{10}{100}$$ × 15320 = ₹ 1532
∴ S.P. = ₹ 15320 + ₹ 1532 = ₹ 16852
∴ $$\frac{22 x}{25}$$ = 16852
⇒ x = $$\frac{16852 \times 25}{22}$$ = ₹ 19150
Hence, the required marked price is ₹ 19150.

Question 8.
A trader buys goods at 19% off the list price. He wants to get a profit of 20% after allowing a discount of 10%. At what price above the list price should he mark the goods?
Solution:
Let list price be 100 and M.P. be x% above the list price.
∴ M.P. = ₹ (100 + x)
∴ C.P. = 100 – 19 = ₹ 81
Profit = 20%
∴ S.P. = C.P. (1 + $$\frac{\text { Profit }}{100}$$)
= 81 (1 + $$\frac{20}{100}$$)
= 81 × $$\frac{6}{5}$$
= ₹ $$\frac{486}{5}$$

Now discount = 10%
∴ S.P. = (100 + x) (1 – $$\frac{10}{100}$$)
= $$\frac{9}{10}$$ (100 + x)
∴ $$\frac{9}{10}$$ (100 + x) = $$\frac{486}{5}$$
⇒ 100 + x = $$\frac{486}{5} \times \frac{10}{9}$$
⇒ 100 + x = 108
⇒ 100 + x = 108
∴ x = 108 – 100 = 8
Hence, the trader should mark his goods 8% above the list price.

Question 9.
A manufacturer allows 4% discount on the marked price of each item. What price must he mark on a dinning table which costs ₹ 400 to assemble so as to make a profit of 20%?
Solution:
Let M.P. of the dinning table be ₹ x.
∴ Discount = $$\frac{4}{100}$$ × x
= ₹ $$\frac{x}{25}$$

∴ S.P. = M.P. – Discount
= x – $$\frac{x}{25}$$
= ₹ $$\frac{24}{25}$$ x

Now C.P. = ₹ 400
and Profit = 20%
∴ S.P. = 400 (1 + $$\frac{20}{100}$$)
= 400 × $$\frac{120}{100}$$
= ₹ 480
∴ $$\frac{24}{25}$$ x = 480
∴ x = $$\frac{480 \times 25}{24}$$ = ₹ 500
Hence, the M.P. of the dinning set = ₹ 500.

Question 10.
A man spends 10% of the cost price as overheads and marks his goods 20% above the total cost price. He allows 10% discount. What is his profit on the article which he sold for ₹ 594?
Solution:
Let C.P. be ₹ x. Hence, the required profit = 18.8%.

Question 11.
How much a shopkeeper must mark his goods so that after allowing a discount of 25% on the marked price, he gains 20%, if the cost price of the goods is ₹ 20,000?
Solution:
Let the M.P. be ₹ x.
Discount = 25% on M.P.
= $$\frac{25}{100}$$ × x
= ₹ $$\frac{x}{4}$$

∴ S.P. = M.P. – Discount
= x – $$\frac{x}{4}$$
= ₹ $$\frac{3 x}{4}$$
C.P. = ₹ 20,000
and Gain = 20%
∴ S.P. = C.P. (1 + $$\frac{\text { Gain }}{100}$$)
$$\frac{3 x}{4}$$ = 20000 (1 + $$\frac{20}{100}$$)
$$\frac{3 x}{4}$$ = 20000 × $$\frac{6}{5}$$
x = 20000 × $$\frac{6}{5} \times \frac{4}{3}$$
= ₹ 32000
Hence, the required marked price is ₹ 32000.

Question 12.
If M.P. = ₹ 650 and discount = 10%, then S.P. is:
(a) ₹ 640
(b) ₹ 550
(c) ₹ 560
(d) ₹ 585
Solution:
M.P. = ₹ 650
Discount = $$\frac{10}{100}$$ × 650 = ₹ 65
∴ S.P. = M.P. – Discount
= ₹ 650 – ₹ 65 = ₹ 585
Hence, (d) is correct.

Question 13.
Kamal bought a wrist watch for ₹ 2200 and sold it for ₹ 1980. His loss % is:
(a) 10%
(b) 20%
(c) 11%
(d) 15%.
Solution:
C.P. = ₹ 2200
S.P. = ₹ 1980
Loss = C.P. – S.P. = ₹ 2200 – ₹ 1980
= ₹ 220
∴ Loss % = $$\frac{220 \times 100}{2200}$$ = 10%
Hence, (a) is correct.

Question 14.
Ankit sold two jeans for ₹ 990 each. On one he gains 10% and on the other he loses 10%. Find his gain or loss per cent in the whole transaction.
Solution:
Let C.P. of first jeans be ₹ x.
Gain = $$\frac{10}{100}$$ × x
= ₹ $$\frac{x}{10}$$
∴ S.P. = ₹ (x + $$\frac{x}{10}$$)
= ₹ $$\frac{11 x}{10}$$
∴ $$\frac{11 x}{10}$$ = 990
⇒ x = $$\frac{990 \times 10}{11}$$
= ₹ 900

Let C.P. of the other jeans be ₹ y.
Loss = $$\frac{10}{100}$$ × y
= ₹ $$\frac{y}{10}$$
∴ S.P. = ₹ (y – $$\frac{y}{10}$$)
= ₹ $$\frac{9 y}{10}$$
∴ $$\frac{9 y}{10}$$ = 990
⇒ y = $$\frac{990 \times 100}{9}$$
= ₹ 1100

∴ Total C.P. of the two jeans = ₹ x + ₹ y
= ₹ 900 + ₹ 1100
= ₹ 2000
and Total S.P. = 2 × 990
= ₹ 1980
∴ Loss = C.P – S.P
= ₹ 2000 – ₹ 1980
= ₹ 20
∴ Loss % = $$\frac{20 \times 100}{2000}$$ = 1%
Hence the loss % = 1 %.

Question 15.
The marked price of a double bed is ₹ 9575. A shopkeeper allows a discount of 12% on its marked price and still gains 10%. Find the cost price of the double bed.
Solution:
M.P. = ₹ 9575
Discount = 12% of M.P.
= $$\frac{12}{100}$$ × 9575
= ₹ 1149
∴ S.P. = M.P. – Discount
= ₹ 9575 – ₹ 1149 = ₹ 8426
Gain = 10%
∴ S.P. = C.P. (1 + $$\frac{\text { Gain }}{100}$$)
8426 = C.P. (1 + $$\frac{10}{100}$$)
8426 = C.P.× $$\frac{11}{10}$$
C.P. = $$\frac{8426 \times 10}{11}$$
= ₹ 7660
Hence, the cost price of the double bed is ₹ 7660.

Question 16.
Meera bought an A.C. for ₹ 22000 including a VAT tax of 10%. Find the price of the A.C. before VAT was added.
Solution:
Let the price of the A.C. before the VAT added be ₹ x.
∴ VAT = $$\frac{10}{100}$$ × x
= ₹ $$\frac{x}{10}$$
∴ Price of the A.C.including VAT = ₹ x + ₹ $$\frac{x}{10}$$
= ₹ $$\frac{11 x}{10}$$
∴ $$\frac{11 x}{10}$$ = 22,000
= 22,000
⇒ x = 22,000 × $$\frac{10}{11}$$
= 2000 × 10 = ₹ 20,000
Hence, the required cost is ₹ 20,000.

Question 17.
Rohan bought some cricket balls at the rate of ₹ 250 for 4 balls and sold them at the rate of ₹ 340 for 5 balls. Find his gain or loss per cent.
Solution:
C.P. of 4 balls = ₹ 250
and S.P. of 5 balls = ₹ 340
∴ S.P. of 4 balls = ₹ 340 × $$\frac{4}{5}$$
= ₹ 272
∴ Gain = ₹ 272 – ₹ 250 = ₹ 22
∴ Gain % = $$\frac{22}{250}$$ × 100 = 8.8%
Hence, the required gain = 8.8%.

Multiple Choice Questions:

Question 1.
If S.P. = ₹ 640 and profit = 28%, then C.P. is _________
(a) ₹ 450
(b) ₹ 500
(c) ₹ 550
(d) ₹ 575
Solution:
(b) ₹ 500

Question 2.
List price = ₹ 16925, Sales Tax = 6%, then the price including S.T. is _________
(a) ₹ 17940.50
(b) ₹ 17940
(c) ₹ 17950
(d) ₹ 17945
Solution:
(a) ₹ 17940.50

Question 3.
M.P. = ₹ 1375, S.T. = 4%, then the total cost is _________
(a) ₹ 1425
(b) ₹ 1430
(c) ₹ 1435
(d) ₹ 1420
Solution:
(b) ₹ 1430

Question 4.
C.P. = ₹ 5500, Rebate = 5%, S.T. = 8%, then the amount to be paid is _________
(a) ₹ 5640
(b) ₹ 5642
(c) ₹ 5645
(d) ₹ 5643
Solution:
(d) ₹ 5643

Question 5.
S.P. = ₹ 17985, S.T. = 9%, then the list price is _________
(a) ₹ 16500
(b) ₹ 16575
(c) ₹ 16600
(d) ₹ 16590
Solution:
(a) ₹ 16500