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Test: Ratio And Proportion, Indices, Logarithms - 3 - CA Foundation MCQ


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30 Questions MCQ Test - Test: Ratio And Proportion, Indices, Logarithms - 3

Test: Ratio And Proportion, Indices, Logarithms - 3 for CA Foundation 2024 is part of CA Foundation preparation. The Test: Ratio And Proportion, Indices, Logarithms - 3 questions and answers have been prepared according to the CA Foundation exam syllabus.The Test: Ratio And Proportion, Indices, Logarithms - 3 MCQs are made for CA Foundation 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Ratio And Proportion, Indices, Logarithms - 3 below.
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Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 1

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

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 1

2x 3x 5z = 360
factorise 360 and you will get 360 = 23x32x51
 2x 3x 5z = 23x32x51
so x=3 , y=2 , z=1

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 2

Find the value of [log10 25 - log10(23) + log10(4)2]

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 2

= [log10 25 - log10(23) + log10(4)2]
= (1.397940009 - 0.903089987 +  1.204119983)

= 1.698970005

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Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 3

If 2x-2x-1=4 then xx is equal to : 

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 3

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

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 4

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

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 4

49+a=3
68+a  4
4x(49+a)=3(68+a)
196+4a=204+3a
a=8

Test: Ratio And Proportion, Indices, Logarithms - 3 - 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:

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 5

Let's denote:

  • A's investment = Rs. 1,26,000
  • B's investment = Rs. 84,000
  • C's investment = Rs. 2,10,000

The total investment is the sum of their individual investments: Total investment = Rs. 1,26,000 + Rs. 84,000 + Rs. 2,10,000 = Rs. 4,20,000

Now, we find the ratio of each person's investment to the total investment:

  • A's ratio = Rs. 1,26,000 / Rs. 4,20,000 = 3/10
  • B's ratio = Rs. 84,000 / Rs. 4,20,000 = 1/5
  • C's ratio = Rs. 2,10,000 / Rs. 4,20,000 = 1/2

Now, we multiply each person's ratio by the total profit to find their share of the profit:

  • A's share = (3/10) * Rs. 2,42,000 = Rs. 72,600
  • B's share = (1/5) * Rs. 2,42,000 = Rs. 48,400
  • C's share = (1/2) * Rs. 2,42,000 = Rs. 1,21,000
Test: Ratio And Proportion, Indices, Logarithms - 3 - 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

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 6

Given a:b=2:3,b:c=4:5,c:d=6:7

a:b=2×8:3×8=16:24   [ Multiplying by 8 ]
b:c=4×6:5×6=24:30   [ Multiplying by 6 ]  
c:d=6×5:7×5=30:35   [ Multiplying by 5 ]
so
a:b:c:d=16:24:30:35

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 7

Log4 (x2+x) - log4 (x+1) = 2. Find x

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 7

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 8

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

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 8

- Let the fourth proportional be y.
- According to the concept of proportionality, x:2x :: (x+1):y
- This can be written as x/2x = (x+1)/y
- Cross multiplying, we get y = 2(x+1)
- Simplifying, we get y = 2x + 2

Therefore, the fourth proportional to x, 2x, and (x+1) is 2x+2, which is option C.
so just multiply x+1 by 2=2(x+1)=2x+2

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 9

If x=31/3+3-1/3 then find value of 3x3-9x

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 10

If loga b + loga c=0 then

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 11

The value of log2 (log5 625) is :​

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 11

Let log5 625 = x.

Then, 5x = 625 = 54 or x = 4.

Let log2(log5 625) = y.

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

∴ log2(log5 625) = 2.

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 12

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

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 12

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

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 13

Find the sub-duplicate ratio of 81 : 64 ?

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 13

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

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 14

 The sub duplicate ratio of 25:36 is

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 14


25:36
√25 : √36
5 : 6

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 15

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

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 15

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 16

 The sub triplicate ratio of 8:27 is 

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 16

Substitute the given ratio into the formula for the sub-triplicate ratio.
a∶b
√a∶√b
√8 : √27
2:3

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 17

The triplicate ratio of 2:3 is

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 17

The triplicate ratio of 2:3 is 
(2/3)3   =    8/27

Test: Ratio And Proportion, Indices, Logarithms - 3 - 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: 

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 18

      Option 4: 50, 70

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 19

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

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 19

The antecedent is the numerator of the fraction, and the consequent is the denominator of the fraction.
Let the consequent of the fraction be x, when antecedent is 15.

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 20

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

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 20

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 21

The duplicate ratio of 3:4 is 

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 21

The duplicate ratio of 3:4 is 32:42 = 9:16

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 22

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

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 22

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 )

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 23

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

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 23

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 24

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

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 24

The given ratio is 5:7, where 5 is the antecedent (the first term) and 7 is the consequent (the second term).

The inverse ratio would flip these, becoming 7:5.

If the consequent of the inverse ratio is 5, this confirms that the inverse ratio is indeed 7:5, as the consequent (second term) is 5.

You're asked for the antecedent of the inverse ratio. Since we've established that the inverse ratio is 7:5, the antecedent (first term) is 7.

Therefore, the correct answer is: 7

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 25

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

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 25

2x+7x+11x=180 [ as sum of all angles of triangle is 180 ]
20x=180
x=9
2(9) 7(9) 11(9)
18 ,63, 99

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 26

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

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 26

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

Test: Ratio And Proportion, Indices, Logarithms - 3 - 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 

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 27

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.

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 28

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

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 28

(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

Test: Ratio And Proportion, Indices, Logarithms - 3 - 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

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 29

Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 30

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

Detailed Solution for Test: Ratio And Proportion, Indices, Logarithms - 3 - Question 30

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

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