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Test: Ratio And Proportion, Indices, Logarithms - 3

40 Questions MCQ Test Quantitative Aptitude for CA CPT | Test: Ratio And Proportion, Indices, Logarithms - 3

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Attempt Test: Ratio And Proportion, Indices, Logarithms - 3 | 40 questions in 40 minutes | Mock test for CA Foundation preparation | Free important questions MCQ to study Quantitative Aptitude for CA CPT for CA Foundation Exam | Download free PDF with solutions

QUESTION: 1

If 2^xx 3^yx 5^z = 360 then what is the value of x, y, z?

A.
3, 2, 1
B.
1, 2, 3
C.
2, 3, 1
D.
1, 3, 2

Solution:

QUESTION: 2

Find the value of [log₁₀25 - log₁₀(2³) + log₁₀(4)²]

A.
X
B.
10
C.
1.69
D.
none

Solution:

= [log₁₀25 - log₁₀(2³) + log₁₀(4)²]
= (1.397940009 - 0.903089987 + 1.204119983)

= 1.698970005

QUESTION: 3

If 2^x-2^x-1=4 then x^x is equal to :

A.
7
B.
3
C.
27
D.
9

Solution:

2^x-2^x-1 =4 , then taking common 2^x-1
2^x-1(2-1) = 4 , 2^x-1 =4 ,
2^x-1=2², simplify
x-1 = 2, x = 3 then
x^x= 3³= 27
hence 27 is the required answer

QUESTION: 4

What must be added to each term of the ratio 49:68, so that it becomes 3:4?

A.
3
B.
5
C.
8
D.
9

Solution:

QUESTION: 5

If A, B and C started a business by investing Rs. 1,26,000, Rs. 84,000 and Rs. 2,10,000. If at the end of the year profit is Rs. 2,42,000 then the share of each is:

A.
72,600, 48,400, 1,21,000
B.
48,400, 1,21,000, 72,600
C.
72,600, 49,400, 1,21,000
D.
48,000, 1,21,400, 72,600

Solution:

QUESTION: 6

If A:B = 2:3, B:C = 4:5 and C:D = 6:7, then find the value of A:B:C:D

A.
15:24:30:35
B.
16:24:30:35
C.
17:24:30:35
D.
18:24:30:35

Solution:

QUESTION: 7

Log₄ (x²+x) - log₄ (x+1) = 2. Find x

A.
16
B.
0
C.
-1
D.
none

Solution:

QUESTION: 8

Fourth proportional to x, 2x, (x+1) is:

A.
(x+2)
B.
(x-2)
C.
(2x+2)
D.
(2x-2)

Solution:

QUESTION: 9

If x=3^1/3+3^-1/3 then find value of 3x³-9x

A.
3
B.
9
C.
12
D.
10

Solution:

QUESTION: 10

If log_a b + log_a c=0 then

A.
b=c
B.
b=-c
C.
b=c=1
D.
b and c are reciprocals.

Solution:

QUESTION: 11

The value of log₂ (log₅ 625) is :

A.
2
B.
5
C.
10
D.
15

Solution:

Let log₅ 625 = x.

Then, 5^x = 625 = 5⁴ or x = 4.

Let log₂(log₅ 625) = y.

Then, log₂ 4 = y or 2^y= 4 = 2² or y = 2.

∴ log₂(log₅ 625) = 2.

QUESTION: 12

If A:B=2:5, then (10A+3B):(5A+2B) is equal to

A.
7 : 4
B.
7 : 3
C.
6 : 5
D.
7 : 9

Solution:

A/B = 2/5

so in (10A+3B)/(5A+2B)

divide both numerator and denominator by B

(10A/B +3)/(5A/B +2)

put A/B value

this becomes (10 * 2/5 + 3)/(5 * 2/5 + 2)

=7/4 = 7:4

QUESTION: 13

Find the sub-duplicate ratio of 81 : 64 ?

A.
8 : 9
B.
4 : 9
C.
9 : 8
D.
7 : 8

Solution:

Required sub - duplicate ratio of 81 : 64 = √81 : √64 = 9 : 8

QUESTION: 14

The sub duplicate ratio of 25:36 is

A.
6 : 5
B.
36:25
C.
50: 72
D.
5 : 6

Solution:

QUESTION: 15

The ratio compounded of 2:3, 9:4, 5:6 and 8:10 is

A.
1 : 1
B.
1 : 5
C.
3 : 8
D.
none of these

Solution:

QUESTION: 16

The sub triplicate ratio of 8:27 is

A.
27::8
B.
24:81
C.
2 :3
D.
none of these

Solution:

QUESTION: 17

The triplicate ratio of 2:3 is

A.
8:27
B.
6 : 9
C.
3 : 2
D.
none of these

Solution:

QUESTION: 18

The student of two classes are in the ratio 5:7, if 10 students left from each class, the remaining students are in the ratio of 4:6 then the number of students in each class is:

A.
30, 40
B.
25, 24
C.
40, 60
D.
50, 70

Solution:

QUESTION: 19

The ratio of two quantities is 3:4. If the antecedent is 15, the consequent is

A.
16
B.
60
C.
22
D.
20

Solution:

QUESTION: 20

The ratio compounded of 4:9, the duplicate ratio of 3:4, the triplicate ratio of 2:3 and 9:7is

A.
2 : 7
B.
7 : 2
C.
2 : 21
D.
none of these

Solution:

Step-by-step explanation:

The duplicate ratio of 3:4 is 3^2/4^2 = 9/16.

The triplicate ratio of 2:3 is 2^3/3^3 = 8/27.

Now we have 4 ratios: 4:9, 9:16, 8:27 and 9:7.

We have to calculate the ratio compounded of all these ratios.

That will be (4 x 9 x 8 x 9)/(9 x 16 x 27 x 7) = 2/21.

QUESTION: 21

The duplicate ratio of 3:4 is

A.
?3:2
B.
4 : 3
C.
9 : 16
D.
none of these

Solution:

QUESTION: 22

The ratio compounded of 4:9 and the duplicate ratio of 3:4 is

A.
1 : 4
B.
1 : 3
C.
3 : 1
D.
none of these

Solution:

Option ( a) 1:4 is right.

Explanation:-
Duplicate ratio of 3:4 , will be the square of the ratio, so this will be 9:16

And the compounded ratio will be product of two ratios:-

4:9 * 9:16 => 1:4

( 9 will be cancelled and 16 by 4 )

QUESTION: 23

The recurring decimal 2.7777………….can be expressed as

A.
24/9
B.
22/9
C.
26/9
D.
25/9

Solution:

QUESTION: 24

The ratio of the quantities is 5:7. If the consequent of its inverse ratio is 5, the antecedent is

A.
5
B.
?5
C.
7
D.
none of these

Solution:

QUESTION: 25

The angles of a triangle are in ratio 2:7:11. The angles are

A.
(20⁰,70⁰,90⁰)
B.
(30⁰, 70⁰,80⁰)
C.
(18⁰, 63⁰,99⁰)
D.
none of these

Solution:

QUESTION: 26

If p:q =2:3 and x:y = 4:5, then the value of 5px + 3qy: 10px + 4qy is

A.
71:82
B.
27:28
C.
17:28
D.
none of these

Solution:

Given as :

The ratio are as follows

p : q = 2 : 3

Let The value of p = 2 a ,

Let The value of q = 3 a

And

x : y = 4 : 5

Let The value of x = 4 b

Let The value of y = 5 b

Now, According to question

Let 5 p x + 3 q y : 10 p x + 4 q y = m : n

QUESTION: 27

Two numbers are in the ratio 2:3. If 4 be subtracted from each, they are in the ratio 3:5. The numbers are

A.
(16, 24)
B.
(4, 6)
C.
(2,3)
D.
none of these

Solution:

Two numbers are in the ratio 2:3.

Let the two numbers are 2x and 3x.

If 4 be subtracted from each, they are in the ratio 3:5.

The value of x is 8.

The two numbers are

2x = 2 * 8 = 16

3x = 3 * 8 = 24

Therefore the two numbers are 16 and 24.

QUESTION: 28

If x:y = 3:4, the value of (x²y+xy²):(x³ +y³) is

A.
13:12
B.
12:13
C.
21:31
D.
none of these

Solution:

(x²y+xy²):(x³ +y³) divide boht numerator and denominator by y³

(x²/y² + x/y) / ((x/y)³ + 1)

put value of x/y = 3/4

(9/16 + 3/4) / (27/64 + 1)

= 12/13

QUESTION: 29

P, Q and R are three cities. The ratio of average temperature between P and Q is 11:12 and that between P and R is 9:8. The ratio between the average temperature of Q and R is

A.
22:27
B.
27:22
C.
32:33
D.
none of these

Solution:

QUESTION: 30

The ratio of two numbers is 7:10 and their difference is 105. The numbers are

A.
(200, 305)
B.
(185, 290)
C.
(245, 350)
D.
none of these

Solution:

We don't know the numbers so let it be xX

7x,10x and they said that the difference of two numbers is 105

10x-7x=105

3x=105

X=105/3

X=35

So the numbers are 245,350

QUESTION: 31

Daily earnings of two persons are in the ratio 4:5 and their daily expenses are in the ratio 7:9. If each saves Rs. 50 per day, their daily incomes in Rs. are

A.
(40,50)
B.
(50,40)
C.
(400,500)
D.
none of these

Solution:

QUESTION: 32

The number which when subtracted from each of the terms of the ratio 19:31 reducing it to 1:4 is

A.
15
B.
5
C.
1
D.
none of these

Solution:

QUESTION: 33

If 2s:3t is the duplicate ratio of 2s-p:3t-p then

A.
p²=6st
B.
p=6st
C.
2p=3qy
D.
none of these

Solution:

QUESTION: 34

The ratio compounded of duplicate ratio of 4:5, triplicate ratio of 1:3, sub duplicate ratio of 81: 256 and sub triplicate ratio of 125: 512 is

A.
4 : 412
B.
3 : 32
C.
1 : 12
D.
none of these

Solution:

dupicate ratio of 4:5 = 16:25

triplicate ratio of 1:3 = 9:27

sub-duplicate ratio of 81:256 = 9:16

sub-triplicate ratio of 125:512 = 5:8

compounded ratio=720:86400 = 1:120

QUESTION: 35

The ratio between the speeds of two trains is 7: 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is ?

A.
83.5 km/hr
B.
84.5 km/hr
C.
86.5 km/hr
D.
87.5 km/hr

Solution:

Let the speed of two trains be 7x and 8x km/hr.

Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.

QUESTION: 36

Division of Rs. 324 between X and Y is in the ratio 11:7. X & Y would get Rupees

A.
(204, 120)
B.
(200, 124)
C.
(180, 144)
D.
none of these

Solution:

QUESTION: 37

If a : b = 3:4, the value of (2a+3b) : (3a+4b) is

A.
54:25
B.
8 : 25
C.
17: 24
D.
18: 25

Solution:

a/b=3/4
So,

[(2 x 3k)+(3 x 4k)]/[(3 x 3k)+(4 x 4k)]

= (6k+12k)/(9k+16k)

=18/25.

QUESTION: 38

Anand earns Rs. 80 in 7 hours and Promod Rs. 90 in 12 hours. The ratio of their earnings is

A.
32:21
B.
23:21
C.
8 :9
D.
none of these

Solution:

Earning of Anand in 1 hour=80/7
earning of promod in 1 hour 90/12
so ratio of their earnings =(80/7)/90/12=80*12/90*7=96/63=32/21

QUESTION: 39

If x/2=y/3=z/7, then the value of (2x-5y+4z)/2y is

A.
6/23
B.
23/6
C.
3/2
D.
none of these

Solution:

QUESTION: 40

The ratio of market prices of wheat and paddy is 2:3 and the ratio of quantities consumed in a family is 5:4. Find the ratio of expenditure of wheat and paddy.

A.
6:5
B.
5:6
C.
1:1
D.
8:15