# Exercise :: 4

(b) 150%

(c) 50%

(d) 200%

(e) None of these

**Ans.a**

He gives 800 grams but charges the price of 1000 grams (1 kg) ⇒ on every 800 grams, he gains (1000 – 800) grams i.e. 200 grams.

∴ His gain % = ^{200}⁄_{800} × 100% = 25%

Short cut : Gain % = \(\frac{error}{true \; weight \; - \; error} = 100\%\)

(b) 15 %

(c) 16 %

(d) 20 %

(e) None of these

**Ans.a**

C.P. of 150 calculators

= 150 × 250 + 2500 = 37500 + 2500 = 40000

Labelled price of 150 calculators

= 150 × 320 = 48000

Discount allowed = 5%

∴ S.P. of 150 calculators

= 48000 – 5% = 45600

∴ Profit % = ^{5600}⁄_{40000} × 100 = 14

(b) 800 g

(c) 825 g

(d) 850 g

(e) None of these

**Ans.b**\(\frac{True \; Weight}{False \; weight} = \frac{100 + gain\%}{100 + x}\)

Here S.P. = C. P. ∴ x = 0

⇒ False Weight = \(\frac{1000 \times 100}{125} = 800 \; gm\)

^{1}⁄

_{2}

(b) 25

(c) 21

^{1}⁄

_{2}

(d) 31

^{1}⁄

_{2}

(e) None of these

**Ans.c**

Let cost Price = 100

∴ Marked price = 135

After discount, selling price = 135 – 13.5 = 121.5

∴ Profit% = 121.5 – 100 = 21.5%

(b) 2% gain

(c) 1.5% loss

(d) 2% loss

(e) None of these

**Ans.a**

S.P. of the 1st chair = 500

Gain = 20%

∴ C.P. of the 1st chair = \(\frac{500 \times 100}{100 + 20} = \frac{500 \times 100}{120} = \frac{1250}{3}\)

S.P. of the 2nd chair = 500

Loss = 12%

∴ C.P. of the 2nd chair = \(\frac{500 \times 100}{100 - 12} = \frac{500 \times 100}{88} = \frac{500 \times 25}{22} = \frac{250 \times 25}{11} = \frac{6250}{11}\)

Now S.P. of both the chairs = 1000

C.P. of both the chairs

= \(\frac{1250}{3} + \frac{6250}{11} = \frac{13750 + 18750}{33} = \frac{32500}{33}\)

∴ Net gain = 1000 – ^{32500}⁄_{33} = ^{500}⁄_{33}

⇒ Gain % = \(\frac{\frac{500}{33}}{\frac{32500}{33}} \times 100 = \frac{500}{32500} \times 100\)

= ^{100}⁄_{65} = ^{20}⁄_{13} = 1.5% (To one place of decimal)

(b) 0.0666

(c) 0.0166

(d) 0.0366

(e) None of these

**Ans.a**

Women's shirt comprise 60% of the output.

∴ Men's shirts comprise (100 – 60) = 40% of the output.

∴ Average profit from men's shirt = 8% of 40 = 3.2 out of 40

Overall average profit = 6 out of 100

∴ Average profit from women's shirts = 2.8 out of 60

i.e. 0.0466 out of each shirt.

(b) 200, 300

(c) 224, 336

(d) 200, 336

(e) None of these

**Ans.c**

Here, in whole transaction, there is neither gains nor loss, therefore,

Amount of gain in one watch = Amount of loss in other watch

⇒ 0.15 × CP_{1} = 0.10 × CP_{2}

⇒ \(\frac{CP_{1}}{CP_{2}} = \frac{0.10}{0.15} = \frac{2}{3}\)

Also CP_{1} + CP_{2} = 560

∴ CP_{1} = \(\frac{2}{2 + 3} \times 560 = 224\)

and CP_{2} = 560 – 224 = 336

(b) 1200

(c) 1500

(d) 1700

(e) None of these

**Ans.b**

Let the C.P. of horse = x

Then the C.P. of carriage = (3000 – x)

20% of x – 10% of (3000 – x) = 2% of 3000

⇒ ^{x}⁄_{5} - \(\frac{\left (3000 - x \right )}{10} = 60\)

⇒ 2x - 3000 + x = 600

⇒ 3x = 3600 ⇒ x = 1200

(b) 2200, 5500

(c) 2400, 5000

(d) 2400, 5600

(e) None of these

**Ans.d**

Here, SP_{1} = SP_{2}

⇒ 140 CP_{1} = 60CP_{2} ⇒ \(\frac{CP_{1}}{CP_{2}} = \frac{6}{14} = \frac{3}{7}\)

∴ CP_{1} = \(\frac{3}{\left (3 + 7 \right )} \times 8000 = 2400\)

and CP_{2} = 8000 – 2400 = 5600

(b) 160

(c) 170

(d) 180

(e) None of these

**Ans.b**

Let the C.P. be 100

First S.P. = 115

Second C.P. = 90

Second S.P = 125% of 90 = 112.50

Difference of two selling prices is 115 – 112.50 = 2.50 and C.P. of the article is 100

But actual difference is 4.

∴ C.P. = ^{100}⁄_{2.50} × 4 = 160.