Exercise :: 4


1. A dishonest fruit seller professes to sell his goods at the cost price but weighs 800 grams for a kg weight. Find his gain percent.
(a) 100%
(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 % = 200800 × 100% = 25%

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

2. A shopkeeper purchased 150 identical pieces of calculators at the rate of 250 each. He spent an amount of 2500 on transport and packing. He fixed the labelled price of each calculator at 320. However, he decided to give a discount of 5% on the labelled price. What is the percentage profit earned by him ?
(a) 14 %
(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 % = 560040000 × 100 = 14

3. A dishonest dealer sells his goods at the cost price but still earns a profit of 25% by underweighing. What weight does he use for a kg?
(a) 750 g
(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 = \(\frac{1000 \times 100}{125} = 800 \; gm\)

4. A shopkeeper marks up his goods to gain 35%. But he allows 10% discount for cash payment. His profit on the cash transaction therefore, in percentage, is
(a) 1312
(b) 25
(c) 2112
(d) 3112
(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%

5. A man sold two steel chairs for 500 each. On one he gains 20% and on other, he loses 12%. How much does he gain or lose in the whole transaction?
(a) 1.5% gain
(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 – 3250033 = 50033

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

= 10065 = 2013 = 1.5% (To one place of decimal)

6. A firm of ready made garments makes both men’s and women’s shirts. Its average profit is 6% of the sales. Its profit in men’s shirts average 8% of the sales and women’s shirts comprise 60% of the output. The average profit per sale rupee in women shirts is
(a) 0.0466
(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.

7. A man purchases two watches at 560. He sells one at 15% profit and other at 10% loss. Then he neither gains nor lose. Find the cost price of each watch.
(a) 224, 300
(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 × CP1 = 0.10 × CP2

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

Also CP1 + CP2 = 560

∴ CP1 = \(\frac{2}{2 + 3} \times 560 = 224\)

and CP2 = 560 – 224 = 336

8. A man bought a horse and a carriage for 3000. He sold the horse at a gain of 20% and the carriage at a loss 10%, there by gaining 2% on the whole. Find the cost of the horse.
(a) 1000
(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

x5 - \(\frac{\left (3000 - x \right )}{10} = 60\)

⇒ 2x - 3000 + x = 600

⇒ 3x = 3600 ⇒ x = 1200

9. Two electronic musical instruments were purchased for 8000. The first was sold at a profit of 40% and the second at loss of 40%. If the sale price was the same in both the cases, what was the cost price of two electronic musical instruments?
(a) 2000, 5000
(b) 2200, 5500
(c) 2400, 5000
(d) 2400, 5600
(e) None of these
Ans.d

Here, SP1 = SP2

⇒ 140 CP1 = 60CP2\(\frac{CP_{1}}{CP_{2}} = \frac{6}{14} = \frac{3}{7}\)

∴ CP1 = \(\frac{3}{\left (3 + 7 \right )} \times 8000 = 2400\)

and CP2 = 8000 – 2400 = 5600

10. A man sells an article at a gain 15%. If he had bought it at 10% less and sold it for 4 less, he would have gained 25%. Find the cost price of the article.
(a) 150
(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. = 1002.50 × 4 = 160.