Comparing Quantities Test

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Comparing Quantities Test - 44

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Weekly Quiz Competition

Question 1
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Madan purchases a compact computer system for Rs. 47,700 which includes 10% rebate on the marked price and then 6% Sales Tax on the remaining price. Find the marked price of the computer.

A
$$Rs. 40,000$$

B
$$Rs. 50,000$$

C
$$Rs. 60,000$$

D
$$Rs. 70,000$$

Solution

Let the marked price of the computer=Rs.x
Rebate=10%
Rebate price=$$\frac{10x}{100}=\frac{x}{10}$$
Remaining price=$$x-\frac{x}{10}=\frac{9x}{10}$$
Rate of sales tax=6%
$$\therefore$$Tax on the remaining price$$=6\% of \frac{9x}{10}$$
$$\Rightarrow \frac{6}{100}\times \frac{9x}{10}=\frac{54x}{1000}$$
Price after the tax$$=\frac{9x}{10}+\frac{54x}{1000}$$
$$\Rightarrow \frac{900x+54x}{1000}=\frac{954x}{1000}=\frac{477x}{500}$$
Then according to the question
$$\therefore \frac{477x}{500}=47700$$
$$\Rightarrow x=\frac{47700\times 500}{477}=50,000$$
Question 2
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Directions For Questions

A shopkeeper buys an article at a discount of 30% and pays sales-tax at the rate of 8%. The shopkeeper, in turn, sells the article to a customer at the printed price and charges sales tax at the same rate. If the printed price of the article is Rs. 2,500; find.

...view full instructions

The price paid by the shopkeeper.

A
$$Rs. 2,400$$

B
$$Rs. 2,100$$

C
$$Rs. 1,890$$

D
$$Rs. 1,960$$

Solution

Printed price$$=Rs 2500$$
Discount Rate $$=30 \%$$
Price after discount$$=2500-30\% \quad of \quad 2500$$
$$\Rightarrow 2500-\dfrac{30}{100}\times 2500$$

$$\Rightarrow 2500-750=Rs.1750$$

Rate of sales tax$$=8 \%$$

$$\therefore $$Price paid by the shopkeeper$$=1750+\dfrac{8}{100}\times 1750$$

$$\Rightarrow 1750+140=Rs.1890$$
Question 3
1 / -0

Directions For Questions

A shopkeeper buys an article at a discount of 30% and pays sales-tax at the rate of 8%. The shopkeeper, in turn, sells the article to a customer at the printed price and charges sales tax at the same rate. If the printed price of the article is Rs. 2,500; find.

...view full instructions

The price paid by the customer

A
$$Rs. 2,500$$

B
$$Rs. 2,700$$

C
$$Rs. 2,900$$

D
$$Rs. 3,100$$

Solution

The shopkeeper sells the article to customer at printed price .
Printed price=Rs.2500
Rate of sales tax=8%
$$\therefore$$Price paid by the customer=2500+8% of 2500
$$\Rightarrow 2500+\frac{8}{100}\times 2500$$
$$\Rightarrow 2500+200=Rs.2700$$
Question 4
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Directions For Questions

A shopkeeper buys a camera at a discount of 20% from the wholesaler, the printed price of the camera being Rs. 1,600 and the rate of sales tax is 6%. The shopkeeper sells it to the buyer at the printed price and charges tax at the same rate. Find

...view full instructions

The price at which the camera can be bought from the shopkeeper.

A
$$Rs. 1,396$$

B
$$Rs. 1,496$$

C
$$Rs. 1,596$$

D
$$Rs. 1,696$$

Solution

Printed price=Rs.1600
Rate of sales tax=6%
Total S.P$$=1600+6\% of 1600$$
$$\Rightarrow 1600+\frac{6}{100}\times 1600$$
$$\Rightarrow 1600+96=Rs.1696$$
Hence the price at which camera can be bought from the shopkeeper=Rs.1669
Question 5
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Ashopkeeper sells an article at its list price (Rs. 3000) and charges sales-tax at the rate of 12%. If the VAT paid by the shopkeeper is Rs. 72, at what price did the shopkeeper buy the article inclusive of sale-tax?

A
$$Rs. 2,590$$

B
$$Rs. 2,688$$

C
$$Rs. 2,451$$

D
$$Rs. 2,100$$

Solution

Let the profit of the retailer=Rs.x
VAT paid by the shopkeeper is Rs.72 at the rate of sales tax 12%
$$\therefore$$ 12% of x=72
$$\Rightarrow \frac{12}{100}x=72$$
$$\Rightarrow x=\frac{72\times 100}{12}=Rs.600$$
$$\therefore$$ cost price to the retailer$$=3000-600=Rs.2400$$
Sales tax paid by the retailer=12% of 2400
$$\Rightarrow \frac{12}{100}\times 2400=Rs.288$$
$$\therefore$$Price of the article including sales tax paid by the shopkeeper $$=2400+288=Rs.2688$$
Question 6
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An article is sold at a profit of $$14\%$$. If both the cost price and selling price are Rs. $$132$$ less, the profit would be $$12\%$$ more. Find the cost price.

A
Rs. $$286$$

B
Rs. $$268$$

C
Rs. $$266$$

D
Rs. $$ 276$$

Solution

Let cost price be $$x$$
SP $$= x + 14\% $$ of $$ x=x+\dfrac{14x}{100} = 1.14x$$
If CP and SP were Rs. $$132$$ less, the profit would be $$(14 + 12)\%$$
New, CP $$= (x - 132)$$
SP $$ = 1.14x - 132$$
SP $$-$$ CP $$= 26\%$$ of $$(x - 132)$$
$$1.14x - 132 - x + 132 = \dfrac{26\times (x-132)}{100}$$
$$0.14x \times100 = 26x - 3432$$
$$14x - 26x = -3432$$
$$12x = 3432$$
$$x = 286$$
So, CP was Rs. $$286$$.
Question 7
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A man sells an article at a gain of $$20\%$$. If he had bought it for $$20 \%$$ less and sold it for $$264$$ less, he would have still gain $$20\%$$.The cost price of the article is ?

A
Rs. $$1100$$

B
Rs. $$2400$$

C
Rs. $$2600$$

D
Rs. $$2650$$

Solution

Let C.P. be $$X$$
Hence, S.P. $$= X+20\%$$ of $$X=X+\dfrac{20}{100}\times X= 1.2 X$$
If he had bought it for $$20\%$$ less
Then, new C.P. $$= X - 20\% $$ of $$ X =X-\dfrac{20}{100}X= 0.8X$$
And new S.P. $$ = 1.2X - 264$$
Gain $$= 20\%$$
$$\Rightarrow \dfrac{(1.2X-264)-.8X}{.8X}=\dfrac{20}{100}$$

$$\Rightarrow \dfrac{.4X-264}{.8X}=\dfrac{20}{100}$$

$$\Rightarrow 40x-26400=16x$$

$$\Rightarrow 24x=26400$$

$$\Rightarrow X = 1100$$
Thus, C.P. of the article $$=$$ Rs. $$ 1100$$.
Question 8
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A man bought a chair and sold it at a gain of $$5$$%. If he had bought it at $$5$$% less and sold it for Rs $$45$$ more, he would have gained $$20$$% . Find the cost price of the chair?

A
Rs. $$400$$

B
Rs. $$500$$

C
Rs. $$450$$

D
Rs. $$550$$

Solution

Let CP = x
SP = x + 5% of x = 1.05x
Now,
If he had bought it in 5% less,
CP = x - 5% of x = 0.95x
New SP = 1.05x + 45
New gain = 20% of 0.95x
1.05 + 45 - 0.95x = 20% of 0.95x
0.1x + 45 = 0.19x
0.09x = 45
x = 500
CP = Rs. 500
Question 9
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A man loses $$13 \%$$ by selling a book at a certain price. If he had sold it for Rs. $$9.75$$ more he would have gained $$26\%$$. Find the cost price of the book ?

A
$$25$$

B
$$30$$

C
$$39$$

D
$$42$$

Solution

Let C.P. be $$x$$

S.P. $$= x - 13\%$$ of $$x =x-\dfrac{13}{100}\times x= 0.87 x$$

If he had sold it in Rs. $$9.75$$ more, he had gained,

New S.P. $$= 0.87x + 9.75$$

Then according to the question, we have

$$\Rightarrow 0.87x + 9.75 = x + 26\%$$ of $$ x$$

$$\Rightarrow 0.8x + 9.75 = 1.26x$$

$$\Rightarrow 0.39x = 9.75$$

$$\Rightarrow x = \dfrac{9.75}{0.39}$$

$$\Rightarrow x = 25$$

So, the cost Price was Rs. $$25$$.
Question 10
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A man has to sell pulse at a loss of 10%. If he increases the selling price by Rs 5 per kg, he would make a profit of 15%. Find the cost price and initial selling price per kg of pulse.

A
Rs 20, Rs 18

B
Rs 18, Rs 20

C
Rs 15, Rs 18

D
Rs 18, Rs 15

Solution

Let C.P. $$= x$$
S.P. $$= x - 10\% $$ of $$ x=x-\dfrac{10x}{100}=\dfrac{90x}{100} = 0.9x$$
New S.P. $$= 0.9x + 5$$
Gain $$ =$$ S.P. $$ -$$ C.P.
$$\Rightarrow 15\% $$ of $$ x = 0.9x + 5 - x$$
$$\Rightarrow 0.15x + x - 0.9x=5$$
$$\Rightarrow 0.25x = 5$$
$$\Rightarrow x = \dfrac{5}{0.25 }=$$ Rs. $$20$$
So, initial selling price $$= 20 - 10\% $$ of $$ 20=20-\frac{10}{100}\times 20 =$$ Rs. $$ 18.$$.

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Re-Attempt Weekly Quiz Competition

Comparing Quantities Test - 44

Result

Comparing Quantities Test - 44

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SHARING IS CARING

Question 1

$$Rs. 40,000$$

$$Rs. 50,000$$

$$Rs. 60,000$$

$$Rs. 70,000$$

Solution

Question 2

$$Rs. 2,400$$

$$Rs. 2,100$$

$$Rs. 1,890$$

$$Rs. 1,960$$

Solution

Question 3

$$Rs. 2,500$$

$$Rs. 2,700$$

$$Rs. 2,900$$

$$Rs. 3,100$$

Solution

Question 4

$$Rs. 1,396$$

$$Rs. 1,496$$

$$Rs. 1,596$$

$$Rs. 1,696$$

Solution

Question 5

$$Rs. 2,590$$

$$Rs. 2,688$$

$$Rs. 2,451$$

$$Rs. 2,100$$

Solution

Question 6

Rs. $$286$$

Rs. $$268$$

Rs. $$266$$

Rs. $$ 276$$

Solution

Question 7

Rs. $$1100$$

Rs. $$2400$$

Rs. $$2600$$

Rs. $$2650$$

Solution

Question 8

Rs. $$400$$

Rs. $$500$$

Rs. $$450$$

Rs. $$550$$

Solution

Question 9

$$25$$

$$30$$

$$39$$

$$42$$

Solution

Question 10

Rs 20, Rs 18

Rs 18, Rs 20

Rs 15, Rs 18

Rs 18, Rs 15

Solution

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