Comparing Quantities Test

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Comparing Quantities Test - 7

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Weekly Quiz Competition

Question 1
1 / -0

If the price of a magazine is decreased by 15%, the number of magazines sold increases by 35%. What is the increase in the total revenue?

A
20.75%

B
18.75%

C
15.75%

D
14.75%

Solution

Let the price of a magazine be Rs. 100.
Original sales of magazines = 100 items
Then,
Total revenue = 100 × 100 = 10,000
Now, the price is decreased by 15%.
Therefore, new price = 85
And the number of magazines sold increases by 35%.
Total number of magazines sold = 135
Therefore, new revenue = 85 × 135
= 11,475
Now, increase in revenue =
= 14.75%
Question 2
1 / -0

If a number m is 20% less than another number n, and n is 20% more than 140, then m is equal to ________.

A
123.4

B
134.4

C
145.8

D
146.9

Solution

It is given that m = n - 20% of n

Also,
n = 140 + 20% of 140
= 140 + 28
n = 168

m =
m = 134.4
Question 3
1 / -0

If 73% of k is 146, then k is equal to

A
180

B
190

C
200

D
210

Solution

73% of k = 146

k = 200
Question 4
1 / -0

A certain number is increased by 15% and then the result obtained is decreased by 20%. Find the net percentage increase or decrease in the number.

A
5% decrease

B
6% increase

C
7% increase

D
8% decrease

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 a product is of its cost price, then the profit% in the transaction is ________.

A
20%

B
24%

C
25%

D
30%

Solution

Let the CP of the product be Rs. X.
SP of the product = X
Profit = SP - CP
=X - X
=
Profit% =
₌ _{= 25%}
Question 6
1 / -0

If 40% of 360 is twice the y% of 960, then the value of y is _____.

A
7.5

B
8.5

C
9.5

D
10.5

Solution

We have
40% of 360 = 2(y% of 960)

= 72
y =
y = 7.5
Question 7
1 / -0

p is 10% of q, and q is 36% of r. If p = 720, find the respective values of q and r.

A
7,500; 25,000

B
7,200; 20,000

C
7,600; 25,000

D
7,700; 27,000

Solution

We have p = 720
According to the question:
p is 10% of q.
720 =
q = 7,200
Also, q is 36% of r.
7,200 =
r = 20,000
Question 8
1 / -0

If 15.6% of 178 = 60% of z, then z equals

A
56.28

B
48.25

C
46.28

D
60.77

Solution

27.768 =
z = 46.28
Question 9
1 / -0

Find the sum invested at y% for y years if the simple interest is Rs. 2y.

A

B

C

D

Solution

SI = Rs. 2y
Rate = y%
Time = y years

SI =

2×y =

P =
Question 10
1 / -0

The simple interest on a certain amount is of the principal. If the number denoting the rate of interest and time is x, find the rate of interest at which the principal is lent out.

A
5.9%

B
6.7%

C
7.2%

D
8.4%

Solution

Let principal = Rs. P
Rate of interest = x%
Time = x years
According to the question,
SI = P
P =
= x²

x² = 35
x = 5.9%
Question 11
1 / -0

A laptop costs Rs. 24,000. After applying a discount, it is priced at Rs. 20,000. What is the percentage discount offered on the laptop?

A
13.33%

B
15.22%

C
16.67%

D
18.12%

Solution

M.P. = Rs. 24,000
S.P. = Rs. 20,000
Discount = M.P. - S.P. = Rs. 4000
Thus, discount % = × 100
= × 100
= 16.67%
Question 12
1 / -0

2 candidates contest an election. One of them gets 35% of the total votes cast and loses by 810 votes. What is the total number of votes cast in the election?

A
2700

B
8100

C
2314

D
6500

Solution

Losing candidate gets 35% votes cast.
Therefore, winning candidate got = (100 - 35) = 65%
So, losing candidate lost by 65 - 35 = 30% votes (Percentage of votes lost)
Also, the losing candidate lost by 810 votes (Votes lost)

So,

= 2700 votes
Question 13
1 / -0

Rohan bought a book at of its original cost and sold it for an amount 5% higher than its original cost. Find his profit percentage.

A
175.2%

B
162.5%

C
153.8%

D
141.5%

Solution

Let the original cost of the book be Rs. 100.

Then, C.P. of book = × 100 = Rs. 40

Also, S.P. of book for Rohan = 100 + 5% of 100 = 100 + 5 = Rs. 105

Gain % =× 100 = × 100
= × 10 = 162.5%
Question 14
1 / -0

Rajiv deposits Rs. 20,000 in a bank at 10% per annum for one year. If the interest is compounded half yearly, then what amount of money will Ram get at the end of the year?

A
Rs. 22,050

B
Rs. 22,500

C
Rs. 25,000

D
Rs. 25,500

Solution

Principal = Rs. 20,000
Rate = 10% per annum
i.e. 5% half yearly
Time = 1 year = 2 half years
Amount = 20,000= Rs. 22,050
Question 15
1 / -0

Ram sells his car and gets Rs. 30,000 as the down payment from the buyer which is 3% of the price of the car. What is the total price of the car?

A
Rs. 3,00,000

B
Rs. 9,00,000

C
Rs. 10,00,000

D
Rs. 12,00,000

Solution

Let P be the price of the car.
Down payment = Rs. 30,000
According to question
3% of P = 30,000
× P = 30,000
P =
P = Rs. 10,00,000
Question 16
1 / -0

Mohit bought an iPhone from Sharan on credit. If the cost of the iPhone was Rs. 30,000 and the rate of interest was 20% per annum compounded half yearly, find the interest paid by Mohit after 2 years.

A
Rs. 48,923

B
Rs. 43,923

C
Rs. 53,923

D
Rs. 59,323

Solution

Principal = Rs. 30,000

Rate = 20% per annum = 10% half yearly

Time = 2 years = 4 half years
Amount =

= 30,000 × (1.1) × (1.1) × (1.1) × (1.1)

= Rs. 43,923
Question 17
1 / -0

Rahul buys 30 kg of curd at Rs. 20 per kg and mixes it with 50 kg of curd at Rs. 24 per kg. At what rate should he sell the mixed curd to gain 24%?

A
Rs. 27.9

B
Rs. 25

C
Rs. 24.5

D
Rs. 22

Solution

CP of 30 kg of the first type of curd = 30 × 20 = Rs. 600

CP of 50 kg of the second type of curd = 50 × 24 = Rs. 1200

Total cost price = Rs. 1800

Gain = 24%

SP =× CP
= × 1800 = Rs. 2232
Total SP of 80 kg of curd = Rs. 2232

SP of 1 kg curd == Rs 27.9
Question 18
1 / -0

A shopkeeper, by selling 13 Titan watches, earns a profit equal to the selling price of 3 Titan watches. Calculate his profit percentage?

A
30%

B
23%

C
46%

D
16%

Solution

Let x be the selling price of 1 Titan watch.
SP = 13x
Profit = 3x
CP = SP - Profit = 10x

Profit % = × 100

= × 100 = 30%

Hence, option 1 is correct.
Question 19
1 / -0

When an article is sold at 20% discount, the selling price is Rs. 24. What will be the selling price when the discount is 30%?

A
Rs. 25

B
Rs. 23

C
Rs. 21

D
Rs. 20

Solution

Let the marked price of the article be x.
So, the selling price, x = 24
x = Rs. 30
When 30% discount is given, the selling price = 30 × = Rs. 21
Question 20
1 / -0

A store is offering "Buy 3, Get 1 Free". What is the net percentage discount being offered by the store?

A
20%

B
25%

C
30%

D
33%

Solution

Let the price of the product be Rs. 100.
Cost of 3 products = Rs. 100 3 = Rs. 300
Cost of 4 products = Rs. 100 4 = Rs. 400
Net discount percentage = [(Discount amount )/(Total Price)] × 100

= = 25%

Question 21

1 / -0

Find the INCORRECT match.

	Principal (Rs.)	Rate (%)	Time (T)	Compound Interest (Rs.)
(A)	90,000	8	2 years	14,976
(B)	25,000	20	3 years	18,200
(C)	6,000	10	2 years	1,260
(D)	5,000	20	4 years	5,378

(A)

(B)

(C)

(D)

Solution

Case 1:
CI = A - P = = 90,000(1.08 × 1.08 - 1)
= 90,000(1.1664 - 1)
= 90,000(0.1664)
= Rs. 14,976

Statement A is correct.

Case 2:
CI = A - P =
= 25,000(1.2 × 1.2 × 1.2 - 1)
= 25,000(1.728 - 1)
= 25,000(0.728)
= Rs. 18,200

Statement B is correct.

Case 3:
CI = A - P = = 6,000(1.10 × 1.10 - 1)
= 6,000(1.21 - 1)
= 6,000(0.21)
= Rs. 1,260

Statement C is correct.

Case 4:
CI = A - P =
= 5,000(1.2 × 1.2 × 1.2 × 1.2 - 1)
= 5,000(2.0736 - 1)
= 5,000(1.0736)
= Rs. 5,368

Statement D is incorrect.

Question 22
1 / -0

Calculate the compound interest (approximate) on Rs. 70,000 for a period of 2 years at 15% per annum if it is

i) compounded annually
ii) compounded half-yearly

A
i) Rs. 22,575; ii) Rs. 23,450

B
i) Rs. 23,450; ii) Rs. 22,575

C
i) Rs. 33,482; ii) Rs. 22,575

D
i) Rs. 23,482; ii) Rs. 32,575

Solution

(i) Compounded annually:
P = Rs. 70,000
n = 2 years
r = 15%
C.I. = ?

A =
A = 70000 × 1.15 × 1.15
= 92,575
= Rs. 92,575
C.I. = Amount – Principal = 92,575 - 70,000 = Rs. 22,575

(ii) Compounded half-yearly:
P = Rs. 70,000
n = 4 years
r = 7.5%
C.I. = ?
A = A = 70,000 × 1.075 × 1.075 × 1.075 × 1.075
≈ 70,000 × 1.335
= Rs. 93,450
C.I. = Amount – Principal = Rs. 93,450 - 70,000 = Rs. 23,450
Question 23
1 / -0

The difference between simple interest and compound interest is Rs. 256 and the principal amount has been invested for 2 years at the rate of 8%. What could be the principal amount?

A
Rs. 4,000

B
Rs. 40,000

C
Rs. 44,000

D
Rs. 45,000

Solution

Let the principal amount be x.

S.I. = =
C.I. = = Therefore, - = 256

= 256

= 256

x =
x = Rs. 40,000

Principal = Rs. 40,000.
Question 24
1 / -0

State True or False for the following statements and mark the correct answer choice.

(A) Simple interest on a sum of money gets doubled in 5 years at 20% per annum.
(B) A man buys 200 oranges for Rs. 1000. To get a profit of 25%, he should sell 16 oranges for Rs. 100.
(C) On selling a watch for Rs. 2000, Raghav incurs a loss of 20%. So, to make a profit of 50%, he should sell the watch for Rs. 3750.
(D) The profit made by selling a table tennis bat for Rs. 652 is as much as the loss incurred when it is sold for Rs. 544. Then the cost price of the table tennis bat is Rs. 598.

A
True, False, True, False

B
True, True, False, True

C
True, True, False, False

D
True, True, True, True

Solution

Case 1:

R = ?
Let P be Rs. 100.
T = 5 years
A = Rs. 200
SI = Rs. 100

SI =
100 =
R = 20%

Case 2:

Cost price of 200 oranges = Rs. 1000
Cost price of 1 orange = (1000/200) = Rs. 5
Selling price of 1 orange = 5 × 1.25= Rs. 6.25
In Rs. 100, number of oranges that can be sold = × 100 = 16
Hence, 16 oranges can be sold for Rs. 100 at a profit of 25%.

Case 3:

Loss percentage = [(CP – SP)/CP] × 100
CP = Rs. 2500
For 50% profit:
Profit percentage = [(SP – CP)/CP] × 100
SP = Rs. 3750

Case 4:

Let CP be x.
Profit = 652 - x and Loss = x - 544
According to the question:
652 - x = x - 544
1196 = 2x
x = 598

Question 25

1 / -0

Match the following:

I	II
(a) At what rate of simple interest will Rs. 3600 yield Rs. 900 over a time span of 3 years?	(i) 6.6%
(b) The compound interest on a certain sum of money at 5% p.a. for 2 years is Rs. 246. What will be the simple interest on the same sum for 3 years at 6% p.a.?	(ii) %
(c) Kaushal lent Rs. 8000 to Piyush for 4 years and Rs. 4000 to Hitesh for 2 years on simple interest at the same rate of interest and received Rs. 2640 in total from both persons as interest. What was the rate of interest per annum?	(iii) Rs. 432
(d) The compound interest on a principal for a period of two years at 5% p.a. is Rs. 10 more than the simple interest on the same principal for the same period at the same rate of interest. Calculate the principal.	(iv) Rs. 4000

(a) - (ii), (b) - (iii), (c) - (i), (d) - (iv)

(a) - (i), (b) - (iv), (c) - (ii), (d) - (iii)

(a) - (i), (b) - (iii), (c) - (ii), (d) - (iv)

(a) - (ii), (b) - (iv), (c) - (i), (d) - (iii)

Solution

(a) S.I. = Rs. 900

P = Rs. 3600

Time = 3 years

Rate = R%

%

(b) Let the principal be P.

C.I. = A - P
246 = On solving, we get:

P = Rs. 2400

Now, S.I. =

= = Rs. 432

(c) Let the rate of interest per annum be x%.

Simple interest on Rs. 8000 for 4 years at x% + Simple interest on Rs. 4000 for 2 years at x% = Rs. 2640

320x + 80x = 2640

400x = 2640

x = = 6.6%

Hence, the rate of interest per annum is 6.6%.

(d) Let the principal be P.

Rate = 5%

Time = 2 years

S.I. = =
C.I. =

C.I. - S.I. = 10

On solving, we get:

P = Rs. 4000

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Re-Attempt Weekly Quiz Competition

Comparing Quantities Test - 7

Result

Comparing Quantities Test - 7

Score

-

Rank

-

SHARING IS CARING

Question 1

20.75%

18.75%

15.75%

14.75%

Solution

Question 2

123.4

134.4

145.8

146.9

Solution

Question 3

180

190

200

210

Solution

Question 4

5% decrease

6% increase

7% increase

8% decrease

Solution

Question 5

20%

24%

25%

30%

Solution

Question 6

7.5

8.5

9.5

10.5

Solution

Question 7

7,500; 25,000

7,200; 20,000

7,600; 25,000

7,700; 27,000

Solution

Question 8

56.28

48.25

46.28

60.77

Solution

Question 9

Solution

Question 10

5.9%

6.7%

7.2%

8.4%

Solution

Question 11

13.33%

15.22%

16.67%

18.12%

Solution

Question 12

2700

8100

2314

6500

Solution

Question 13

175.2%

162.5%

153.8%