Comparing Quantities Test

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Comparing Quantities Test - 6

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Question 1
1 / -0

When the price of a product is decreased by 15%, the number of products sold increases by 35%. What is the increase in total revenue?

A
14.75%

B
20.75%

C
15.75%

D
14.25%

Solution

Let the price of a product be Rs. 100 and the original sales of product be 100 items.
Then, total revenue = 100 × 100 = 10,000
Now, the price is decreased by 15%.
Therefore, new price = 100 - 15% of 100 = 85
Also, the number of pieces sold is increased by 35%.
Total number of pieces sold = 100 + 35% of 100 = 135
Therefore, new revenue = 85 × 135 = 11,475
Now, increase in revenue =
= 14.75%
Question 2
1 / -0

If a number x is 20% less than another number y, and y is 20% more than 140, then x is equal to

A
120.31

B
134.40

C
130.52

D
125.33

Solution

It is given that
x = y - 20% of y
= y - (2/10)y

Also,
y = 140 + 20% of 140
= 140 + 28
y = 168
∵
∴
x = 134.4
Question 3
1 / -0

If 64% of p is 128, then the value of p is

A
400

B
300

C
200

D
450

Solution

We have,
64% of p = 128

p =
p =
p = 200
Question 4
1 / -0

A number is increased by 15% and then decreased by 20%. Find the net increase or decrease percent.

A
7%

B
12%

C
10%

D
8%

Solution

Let the number be 100.
Increased number = 100 + 15% of 100
= 100 + 15 = 115
Now, this number is decreased by 20%.
New number = 115 - 20% of 115
= 92
Net decrease = 100 - 92 = 8
Net % decrease
=
= 8%
Question 5
1 / -0

If the selling price of an article is of its cost price, then the profit percent in the deal is

A
30%

B
35%

C
25%

D
20%

Solution

Let the CP of the article be Rs. X.
SP of the article = Rs.X
Profit = SP - CP
=X - X
=
Profit % =

= 25%
Question 6
1 / -0

If 20% of 180 is equal to twice the y% of 480, then the value of y is

A
7.75

B
4.55

C
4.75

D
3.75

Solution

We have,
20% of 180 = 2(y% of 480)

= 18
y =
y = 3.75
Question 7
1 / -0

p is 20% of q, and q is 72% of r. If p = 1,440, find the values of q and r, respectively.

A
20,000; 10,000

B
7,200; 15,000

C
7,200; 10,000

D
5,000; 10,000

Solution

We have p = 1,440
According to the question:
p is 20% of q.
So,
1,440 =
q = 7,200
Also, q is 72% of r.
So,
7,200 =
r = 10,000
Hence, q = 7,200 and r = 10,000
Question 8
1 / -0

If 31.2% of 356 = 30% of z, then z equals

A
370.24

B
340.24

C
270.24

D
470.24

Solution

111.07 =
z = 370.24
Question 9
1 / -0

Find the sum invested at p% for p years if the simple interest is Rs. 3p.

A

B

C

D

Solution

SI = Rs. 3p
Rate = p%
Time = p years
SI =
3p =
P =
Question 10
1 / -0

The simple interest on a certain amount is of the principal. The rate of interest at y% per annum is equal to y years. Find the rate percent.

A
5.68%

B
7.69%

C
5.24%

D
9.98%

Solution

Let the principal be Rs. P.
Rate of interest = T = y%
According to the question:
SI = P
Now, ^So,
P =

y² = 59.09
y = 7.69% (approx.)
Question 11
1 / -0

A blanket worth Rs. 6500 is on sale at Rs. 4500. What percent discount is offered during sale?

A
30.77%

B
35.54%

C
40.76%

D
50.25%

Solution

MP = Rs. 6500
SP = Rs. 4500
Discount = MP - SP
= 6500 - 4500
= Rs. 2000
Thus, Discount % =
=
= 30.77% (approx.)
Question 12
1 / -0

The number of fishes in a lake is decreasing due to pollution of sea water and environment. The present number of fishes is 8,32,140. Last year 5% of fishes died, and last to last year it was 8%. What was the approximate number of fishes two years ago?

A
9,52,120

B
9,52,106

C
9,52,850

D
8,52,105

Solution

Let the number of fishes two years ago be X,
Number of fishes remained after one year =
Number of fishes remained after two years = ()- () ×
Since the population after two years is 8,32,140;

8,32,140 = () - () ×
8,32,140 =
8,32,140 =
8,32,140 × 2000 = 1900X - 152X

X = 9,52,105.632 = 9,52,106 (approx.)

Hence, the number of fishes two years ago was 9,52,106.
Question 13
1 / -0

Anuj purchased a solar water heater at ^th of its actual price and sold it at 10% more than its actual price. Find the profit percent that he made by selling the water heater.

A
40%

B
47.5%

C
37.5%

D
35%

Solution

Let actual price = Rs. 100
Then, cost price of heater for Anuj = Rs. × 100
= Rs. 80
SP of the heater for Anuj
= Rs. 100 + 10% of Rs. 100
= Rs. 110
Profit % = × 100
= 37.5%
Question 14
1 / -0

Suresh invests Rs. 50,000 at 15% per annum for one year. If the interest is compounded thrice a year, then the amount received at the end of year will be

A
Rs. 57,881.75

B
Rs. 57,981.25

C
Rs. 67,881.25

D
Rs. 57,881.25

Solution

Principal, P = Rs. 50,000
Rate, r = 15% p.a. = 5% thrice a year
Time, n = (12/4) = 3
Now,
So, amount =
= Rs. 57,881.25
Question 15
1 / -0

Deepak is doing a business; he gets Rs. 60,000 as a profit which is 10% of the selling price of a old house. At what price does Deepak sell the property?

A
Rs. 1,50,000

B
Rs. 5,50,000

C
Rs. 6,00,000

D
Rs. 4,00,000

Solution

Let the selling price of the house be Rs. X.
Profit made by Deepak = 10% of the selling price
=
Since he receives Rs. 60,000;
= Rs. 60,000
X = 6,00,000
SP of the house = Rs. 6,00,000
Question 16
1 / -0

Ankush purchased a car from Mr. Sharma on credit. If the cost of the car is Rs. 75,000 and the rate of interest is 10% p.a. compounded three times a year, find the interest paid by Ankush after (2/3) years.

A
Rs. 8457.5

B
Rs. 8097.5

C
Rs. 3057.5

D
Rs. 5083.3

Solution

Principal = Rs. 75,000
Rate = 10% p.a.
It is compounded thrice.
Hence, r =% thrice a year
Time, n = 2
Amount = =
= Rs. 80,083.3
So, compound interest = Rs. 80,083.3 - Rs. 75,000 = Rs. 5083.3 (approx.)
Question 17
1 / -0

A store manager purchases 70 kg of wheat at Rs. 15.50 per kg and mixes it with 110 kg of wheat of cost Rs. 18 per kg. At what rate should he sell the mixture to gain 20%?

A
Rs. 18.45

B
Rs. 19.43

C
Rs. 20.43

D
Rs. 15.75

Solution

Cost price of 70 kg wheat of 1^st variety = 15.5 x 70 = Rs. 1085
Cost price of 110 kg wheat of 2^nd variety = 18 x 110 = Rs. 1980
Total CP = 1085 + 1980 = Rs. 3065
Gain = 20%
Now, SP =
== Rs. 3678
Total SP of 180 kg = Rs. 3678
SP of 1 kg = = Rs. 20.43
Hence, he should sell the mixture at Rs. 20.43 per kg to gain 20%.
Question 18
1 / -0

A salesman sold two articles for Rs. 30,000 each. On one he made a profit of 10% and on the other a loss of 15%. Find his overall profit or loss.

A
Loss, Rs. 2566.8

B
Profit, Rs. 3564.2

C
Profit, Rs. 2566.8

D
Loss, Rs. 3056.2

Solution

S.P of 1 article = Rs. 30,000
Gain = 10%
Now,

So, CP = = Rs. 27,272.7
SP of the second article = 30,000 and Loss = 15%
Now,

So, CP = = Rs. 35,294.1

Total CP = Rs. 35,294.1 + Rs. 27,272.7 = Rs. 62,566.8
Total SP = Rs. 30,000 + Rs. 30,000 = Rs. 60,000
Loss = CP - SP
= Rs. 62,566.8 - Rs. 60,000
= Rs. 2566.8
Question 19
1 / -0

A magazine was sold for Rs. 30.5 with a profit of 15%. If it was sold for Rs. 25.75, then what would have been the profit % or loss %?

A
2.75% Loss

B
3.5% Profit

C
2.9% Loss

D
4.5% Profit

Solution

SP of the magazine = Rs. 30.5
Profit % = 15%
CP = × 30.5
= Rs. 26.52
Now, new selling price = Rs. 25.75
Loss = Rs. 26.52 - Rs. 25.75
Loss = Rs. 0.77
Loss % = × 100
= 2.9%
Question 20
1 / -0

If a car costs Rs. 2,75,000 and the value depreciates at the rate of 25% p.a, then the total depreciation after 4 years will be

A
Rs. 1,80,945

B
Rs. 1,87,988

C
Rs. 1,23,000

D
Rs. 1,45,254

Solution

Cost of the car = Rs. 2,75,000
Rate of depreciation = 25%
Depreciated value after 4 years
=
= Rs. 87,011.7
Total depreciation = Rs. 2,75,000 - Rs. 87,011.7
= Rs. 1,87,988.3
= Rs. 1,87,988 (approx.)

Question 21

1 / -0

Select the incorrect match in the following table:

	Principal (Rs.)	Rate %	Time (Years)	Simple Interest (Rs.)
A	5000	10	2	1000
B	6000	20	3	1500
C	4500	5	1	225
D	3000	11.5	2.5	862.5

B

C

D

A

Solution

When P = 6000, R = 20 and T = 3,

= Rs. 3600
Hence, (B) is incorrectly matched.

Question 22

1 / -0

Surbhi pays a simple interest of Rs. 1000 on a sum of Rs. 5000, which she borrows from a bank at a certain rate of interest (R%) for 2 years; and Shruti pays a simple interest of Rs. 1500 on a sum of Rs. 9000 which she borrows at r% for 2 years. What is the rate of interest for both? Choose the correct match using the table given below.

	I (Surbhi's R%)	II (Shruti's r%)
A	25%	15.5%
B	8.3%	10%
C	25%	15.5%
D	10%	8.3%

A

D

C

B

Solution

Rate of interest for Surbhi:

R = 10%
Rate of interest for Shruti:

r = 8.3%

Question 23
1 / -0

The difference between the simple and the compound interest on a certain sum of money at 15% p.a. for 2 years is Rs. 800. Find the sum when the interest is compounded annually.

A
Rs. 45,555.55

B
Rs. 3,455.55

C
Rs. 35,555.55

D
Rs. 3,555.55

Solution

Let P be the principal.
According to the question,
CI - SI = Rs. 800
= 800
0.3225P - 0.3P = 800
0.0225P = 800
P = Rs. 35,555.55
Question 24
1 / -0

State True and False for the given statements.

I. A person makes some profit after selling a jacket at Rs. 850 which is same as loss after selling the same jacket at Rs. 710. The cost of the jacket is Rs. 780.
II. A bike dealer buys a bike for Rs. 9400 and spends Rs. 1600 for its paint job. Now he decides to sell it for Rs. 11,600. His profit percent is 4.5%.
III. A vegetable seller buys a dozen of bananas for Rs. 100. In order to get 20% profit, the seller has to sell 9 bananas for Rs. 100.
IV. A shopkeeper buys a pair of earphones for Rs. 1200. He marks up the price of the earphones by 25% and after that gives a discount of 20%. So, the selling price of the earphones is Rs. 1200.

A
I - True, II - False, III - True, IV - True

B
I - False, II - False, III - False, IV - False

C
I - True, II - True, III - False, IV - False

D
I - True, II - False, III - False, IV - True

Solution

Consider statement I.
Let X be the cost of jacket.
According to the question:
850 – X = X – 710
2X = 1560
X = 780 (True)

Consider statement II.
Cost price (CP) = Rs. (9400 + 1600) = Rs. 11,000
Selling price (SP) = Rs. 11,600
Profit = (SP) - (CP) = Rs. (11,600 – 11,000) = Rs. 600
Profit % = × 100 = 5.45% (False)

Consider statement III.
CP of 12 bananas = Rs. 100
CP of 1 banana = Rs. (100/12)
SP of 1 banana at 20% profit = 120% of Rs. (100/12)
= Rs. 10
For Rs. 100, he should sell = = 10 bananas. (False)

Consider statement IV.
Cost price of the pair of earphones = Rs. 1200
Markup is 25%.
So, marked price = 25% of 1200 + 1200 = = Rs. 1500
Discount = 20%
So, selling price = 1500 - (20% of 1500) = 80% of 1500 = Rs. 1200 (True)

Question 25

1 / -0

Match the following:

Column I	Column II
I. A dealer offers 28% discount while selling a second-hand car and sells it at Rs. 2,52,000. Find the original price of the car (in Rs.).	a) 2,00,000
II. In a tank, there is a mixture of 60 gallons of kerosene and petrol in the ratio 1 : 2. A buyer wants it to be in the ratio 2 : 1. How much kerosene (in gallons) should be added to the mixture to make this ratio?	b) 60
III. An investor invests a certain sum of money in share market for 5 years at the rate of 20% per annum and gets a simple interest of Rs. 2,00,000. Calculate the money invested (in Rs.).	c) 3,50,000

I – c, II – b, III - a

I – a, II – b, III - c

I – b, II – a, III - c

I – b, II – c, III - a

Solution

I. Let the original price be P.
P ×= Rs. 2,52,000
P =

= Rs. 3,50,000

II. Quantity of petrol = 60 × = 40 gallons
Quantity of kerosene = 60 - 40 = 20 gallons
Let the quantity of kerosene added be X.
New ratio = 2 : 1
Petrol : Kerosene =
= =
= 20 + X = 80
X = 60 gallons

III. SI = (PRT)/100

Principal =

= Rs.

= Rs. 2,00,000

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Re-Attempt Weekly Quiz Competition

Comparing Quantities Test - 6

Result

Comparing Quantities Test - 6

Score

-

Rank

-

SHARING IS CARING

Question 1

14.75%

20.75%

15.75%

14.25%

Solution

Question 2

120.31

134.40

130.52

125.33

Solution

Question 3

400

300

200

450

Solution

Question 4

7%

12%

10%

8%

Solution

Question 5

30%

35%

25%

20%

Solution

Question 6

7.75

4.55

4.75

3.75

Solution

Question 7

20,000; 10,000

7,200; 15,000

7,200; 10,000

5,000; 10,000

Solution

Question 8

370.24

340.24

270.24

470.24

Solution

Question 9

Solution

Question 10

5.68%

7.69%

5.24%

9.98%

Solution

Question 11

30.77%

35.54%

40.76%

50.25%

Solution

Question 12

9,52,120

9,52,106

9,52,850

8,52,105

Solution

Question 13

40%

47.5%

37.5%