# Exercise :: 5

(b) 150

(c) 240

(d) 280

(e) None of these

**Ans.a**

Let the CP of the article be x.

Then, SP = ^{105x}⁄_{100}

Now, new CP = ^{95x}⁄_{100} and new SP = ^{105x}⁄_{100} - 1

According to the question

\(\frac{105x}{100} - 1 - \frac{95}{100} = \frac{10 \times 95x}{100 \times 100}\)∴ x = 200

(b) 52.50

(c) 60

(d) 72.50

(e) None of these

**Ans.a**

Let S.P. = x per kg

∴ S.P. of 4 kg = 4x

∴ 4x = \(\frac{100 - 40}{100} \times 300\)

⇒ x = ^{270}⁄_{4} = 67.50

^{1}⁄

_{2}

(b) 11

^{1}⁄

_{9}

(c) 5

^{15}⁄

_{17}

(d) 8

^{2}⁄

_{3}

(e) None of these

**Ans.a**

Let C.P. of one orange = 1

Then C.P. of 8 oranges = 8

S.P of 8 oranges = 9

∴ Gain % = \(\frac{9 - 8}{8} \times 100 = \frac{100}{8} = 12\tfrac{1}{2} \%\)

(b) 20

(c) 25

(d) 30

(e) None of these

**Ans.c**

Let C.P. of 1 article = 1

then C.P. of 25 articles = 25

and S.P. of 25 articles = 20

∴ loss % = \(\frac{25 - 20}{20} \times 100 = 25\%\)

(b) 22

^{1}⁄

_{2}%

(c) 33%

(d) 33

^{1}⁄

_{3}%

(e) None of these

**Ans.d**

Let C.P. of one metre of cloth = 1

then C.P. of 66 metres of cloth = 66

Gain = C.P. of 22 metres = 22

% gain = ^{22}⁄_{66} × 100 = 33^{1}⁄_{3}%

**Shortcut method :**

If on selling ‘x’ articles, a man gains equal to the C.P. of ‘y’ articles, then % gain = ^{y}⁄_{x} × 100

∴ % gain = = ^{22}⁄_{66} × 100 = 33^{1}⁄_{3}%

(b) 25%

(c) 30%

(d) 35%

(e) None of these

**Ans.b**

Loss = C.P. of 66 metres – S.P. of 66 metres

= S.P. of 22 metres

⇒ C.P. of 66 metres = S.P. of 88 metres

% loss = \(\frac{loss}{C.P. \; of \; 66 \; metres} \times 100\)

= \(\frac{S.P. \; of \; 22 \; metres}{C.P. \; of \; 66 \; metres} \times 100\)

= \(\frac{S.P. \; of \; 22 \; metres}{S.P. \; of \; 88 \; metres} \times 100\)

= ^{22}⁄_{88} × 100 = 25%

* Try to solve by shortcut method

(b) 28%

(c) 30%

(d) 35%

(e) None of these

**Ans.b**

Equivalent discount = 10 + 20 - \(\frac{10 \times 20}{100}\)

= 30 – 2 = 28%

(b) 14%

(c) 15%

(d) 18%

(e) None of these

**Ans.c**

Retailer price = list price \(\left ( 1 - \frac{d_{1}}{100} \right )\left ( 1 - \frac{d_{2}}{100} \right )\)

⇒ 122.40 = 160\(\left ( 1 - \frac{10}{100} \right )\left ( 1 - \frac{d_{2}}{100} \right )\)

⇒ \(1 - \frac{d_{2}}{100} = \frac{122.40 \times 100}{160 \times 90} = 0.85\)

⇒ d_{2} = (1 - 0.85) × 100 = 15%

(b) 8%

(c) 15%

(d) 18%

(e) None of these

**Ans.b**

Let the C.P. of the goods be 100

⇒ Marked price of the goods = 120

Discount = 10% ⇒ S.P. is 90% of 120 = 108

∴ Gain = (108 – 100) i.e. 8%.

(b) 20%

(c) 35%

(d) 50%

(e) None of these

**Ans.d**

For same article, \(\frac{100 - d_{1}}{100 - d_{2}} = \frac{100 + g_{1}}{100 + g_{2}}\)

⇒ \(\frac{100 - 25}{100 - 10} = \frac{100 + 25}{100 + g_{2}} \Rightarrow \frac{75}{90} = \frac{125}{100 + g_{2}}\)

⇒ 100 + g_{2} = \(\frac{90 \times 125}{75} = 150\) ⇒ g_{2} = 50%

^{11}⁄

_{13}

(b) 105

^{3}⁄

_{21}

(c) 127

^{1}⁄

_{17}

(d) 95

^{1}⁄

_{21}

(e) None of these

**Ans.c**

SP = 90 × 1.2 = 108

Marked price = ^{108}⁄_{0.85} = 127.05

(b) 66

^{2}⁄

_{3}%

(c) 30%

(d)

^{100}⁄

_{3}%

(e) None of these

**Ans.d**

Let the SP of the article be x

Expenses = 15% of x = 0.15x

Profit = 10% of x = 0.10x

CP = 9 (given)

Therefore, 9 + 0.15x + 0.1x = x ⇒ x = 12

∴ % increase for marked price = \(\frac{12 - 9}{9} \times 100 = \frac{100}{3} \%\)