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All questions of Chapter 1: Ratio and Proportion, Indices, Logarithms for CA Foundation Exam

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 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
Correct answer is option 'A'. Can you explain this answer?

Kavya Saxena answered
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

  • a)
    xy2
  • b)
    x2y
  • c)
    9xy2
  • d)
    none of these
Correct answer is option 'D'. Can you explain this answer?

Deeksha Kesarwani answered
(81x^4y^8)^1/4(3^4x^4y^8)^1/43^4*1/4x^4*1/4y^8*1/43xy^2(d) none of these

Can you explain the answer of this question below:

If x/y = z/w, implies y/x = w/z, then the process is called

  • A:

    Dividendo

  • B:

    Componendo

  • C:

    Alternendo

  • D:

    none of these

The answer is d.

Pallabi Khanna answered
Explanation:

The given equation is x/y = z/w.

To find out if y/x = w/z, we can use the property of cross-multiplication:

- Cross-multiplying the given equation, we get xw = yz.
- Dividing both sides by xyz, we get w/y = z/x.
- Rearranging, we get y/x = w/z.

Therefore, the given equation implies that y/x = w/z.

The process of using cross-multiplication to find equivalent fractions is a basic arithmetic skill and does not have a specific name. Therefore, the answer is d) none of these.

Conclusion:

- The given equation x/y = z/w can be cross-multiplied to get xw = yz.
- Dividing both sides by xyz, we get w/y = z/x, which can be rearranged to y/x = w/z.
- The process of using cross-multiplication to find equivalent fractions does not have a specific name, so the answer is d) none of these.

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
Correct answer is option 'B'. Can you explain this answer?

Manoj Ghosh answered
ii) From the given data, we have x = (3/4)y or 4x = 3y 

iii) (x2y + xy2) :: (x2 + y2) = xy(x + y)/{(x + y)(x2 - xy + y2) = (xy)/(x2 - xy + y2) 
Substituting x = (3/4)y from the above, 
(x2y + xy2) :: (x2 + y2) = (3y2/4)/(9y2/16 - 3y2/4 + y2) = 12/(9 - 12 + 16) = 12/13 

Can you explain the answer of this question below:

If 2x-2x-1=4 then xx is equal to : 

  • A:

    7

  • B:

    3

  • C:

    27

  • D:

    9

The answer is c.

Preeti Khanna answered
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
xx = 33 = 27
hence 27 is the required answer

Can you explain the answer of this question below:

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

  • A:

    16

  • B:

    60

  • C:

    22

  • D:

    20

The answer is d.

Kavya Sharma answered
Given ratio is 3:4 
Let x be measurable since antecedent is 15 = > 3x + 15 = > x =5 the consequent is 4x = 4x5 = 20 
so we have consequent as 20 

The ratio compounded of 4:9, and the duplicate ratio of 3:4,the triplicate ratio of 2:3 and 9:7 is
  • a)
    2:7
  • b)
    7:2
  • c)
    2:21
  • d)
    none of these
Correct answer is 'C'. Can you explain this answer?

Ishani Rane answered
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.

The sum of the ages of 3 persons is 150 years. 10 years ago their ages were in the ratio 7 : 8 : 9. Their present ages are
  • a)
    (45, 50, 55)
  • b)
    (40, 60, 50)
  • c)
    (35, 45, 70)
  • d)
    none of these
Correct answer is option 'A'. Can you explain this answer?

Kavya Sharma answered
their 10years ago age be 7x,8x,9x
so their current age be 7x+10,8x+10,9x+10
7x+10+8x+10+9x+10=120
24x+30=150
24x=120
x=5
present age= 7x+10,8x+10,9x+10
                   =7(5)+10,8(5)+10,9(5)+10
                   =45,50,55

[{(2)1/2 . (4)3/4 . (8)5/6 . (16)7/8 . (32)9/10}4]3/25 is
  • a)
    A fraction
  • b)
    an integer
  • c)
    1
  • d)
    none of these
Correct answer is option 'B'. Can you explain this answer?

Raghavendra Sharma answered
x={[(125)2/3⋅(8)5/6⋅(16)7/8⋅(32)9/10]4}3/25
=[(53⋅2/3⋅23⋅5/6⋅24⋅7/8⋅25⋅9/10)4]3/25=[(52⋅25/2⋅27/2⋅29/2)4]3/25=[(52⋅25/2+7/2+9/2)4]3/25=
=[(52⋅221/2)4]3/25=[58⋅242]3/25=524/25⋅2126/25=524⋅2126−−−−−−−√25=32524⋅2−−−−−√25
x≈154,24190566187577033261129981792
so option B is correct

  • a)
    1
  • b)
    0
  • c)
    5
  • d)
    none of these
Correct answer is option 'B'. Can you explain this answer?

Target Study Academy answered
Let X=(b+c-a);y=(c+a-b);z=(a+b-c)

=(b-c)(b+c-a)+(c-a)(c+a-b)+(a-b)(a+b-c)

=b^2-c^2-ab+ac+c^2-a^2-bc+ab+a^2-b^2-ac+bc

=0

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
Correct answer is option 'B'. Can you explain this answer?

Sameer Rane answered
Here's the solution to your question: 

P /Q = 11 / 12        P / R = 9 / 8

Q / R =   P/R  /   P/Q    =  9/8  /  11/12  = 9*12 / 8*11  = 27/22 

The ratio between the average temperature of Q and R is Q : R  = 27 : 22

Hence, the correct answer is Option B

You can go through Important Formulas & Tips of Ratio and Proportion by going through the doc:

Anand earns Rs. 80 in 7 hours and Promode Rs. 90 in 12 hours. The ratio of their earnings is
  • a)
    32 : 21
  • b)
    23 : 12
  • c)
    8 : 9
  • d)
    none of these
Correct answer is option 'A'. Can you explain this answer?

Pallabi Deshpande answered
Ratio of Anand and Promode earnings = 32 : 21.

Solution:

Anand earns Rs. 80 in 7 hours.

Anand earns Rs. 80/7 in 1 hour.

Promode earns Rs. 90 in 12 hours.

Promode earns Rs. 90/12 in 1 hours.

Ratio of their earnings = 80/7 : 90/12

=> 80 * 12 : 90 * 7

=> 8 * 12 : 9 * 7

=> 96 : 63

=> 32 : 21.

Ratio of their earnings = 32 : 21.

If p : q is the sub duplicate ratio of p–x2 : q–x2 then x2 is
  • a)
    p/p+q
  • b)
    q/p+q
  • c)
    p/p-q
  • d)
    pq/p+q
Correct answer is option 'D'. Can you explain this answer?

Naina Bansal answered
√(p-x2) /(q-x2)  = p/q --(1) 
[Sub- duplicate ratios of, 
  a/b= √a/b] 
Squaring both sides eq. -(1) ; 
(p-x2) /(q-x2) = p2/ q2
q2( p-x2)  = p2(q-x2) 
q2 p - q2 x2  = p2 q - p2 x2
X2 ( p2-q2) = pq (p-q) 
x2 =  pq (p-q) / (p+q) (p-q) 
x2 = pq/p+q
Therefore, option (d) none of these is the correct answer. 

If 2x x 3y x 5z = 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
Correct answer is option 'A'. Can you explain this answer?

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

If x : y = z : w = 2.5 : 1.5, the value of (x+z)/(y+w) is
  • a)
    1
  • b)
    3/5
  • c)
    5/3
  • d)
    none of these
Correct answer is option 'C'. Can you explain this answer?

Dhruv Mehra answered
x/y = 5/3 

x = 5/3 y 

z/w = 5/3 

z = 5/3 w 

x + z = 5/3 y + 5/3 w 

= 5/3( y + w) 

(x + z)/(y + w) = 5/3 

= 1(2/3)

The value of ya–b × yb–c × yc–a × y–a–b is
  • a)
    ya+b
  • b)
    y
  • c)
    1
  • d)
    1/ya+b
Correct answer is option 'D'. Can you explain this answer?

Anu Kaur answered
I'm sorry, but I can't determine the value of "ya" without more information regarding the context. Please provide more details.

The ratio compounded of 4:9, and the duplicate ratio of 3:4,the triplicate ratio of 2:3 and 9:7 is
  • a)
    2:7
  • b)
    7:2
  • c)
    2:21
  • d)
    none of these
Correct answer is option 'C'. Can you explain this answer?

Ishani Rane answered
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.

If x1/p = y1/q = z1/r and xyz = 1, then the value of p+q+r is
  • a)
    1
  • b)
    0
  • c)
    1/2
  • d)
    none of these
Correct answer is option 'B'. Can you explain this answer?

Arya Roy answered
x1/p=y1/q=z1/r=k (say)
⇒ x = kp,y = kq,z = kr
xyz=1 (given)
kp.kq.kr=1
k(p+q+r)=1.
k(p+q+r)=k0
p+q+r = 0

Can you explain the answer of this question below:

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

  • A:

    X

  • B:

    10

  • C:

    1

  • D:

    none

The answer is c.

Kavya Saxena answered
= [log10 25 - log10(23) + log10(4)2]
= (1.397940009 - 0.903089987 +  1.204119983)
= 1.698970005

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 
Correct answer is option 'D'. Can you explain this answer?

Ishani Rane answered
Here is ratio of division is 11:7 so,
X share = 11a and Y is 7a
total 11a + 7a = 18a
18a = 324
 a = 18 
X share = 11a= 198 rs
Y share = 7a= 126 rs

4, *, 9, 13½ are in proportion. Then * is
  • a)
    6
  • b)
    8
  • c)
    9
  • d)
    none of these
Correct answer is option 'A'. Can you explain this answer?

Sahil Malik answered
Given: 4, *, 9, 13 are in proportion.

To find: The value of *

We know that if four numbers a, b, c, and d are in proportion, then:

a : b = c : d

Using this property, we can write:

4 : * = 9 : 13

Cross-multiplying both sides, we get:

4 × 13 = 9 × *

52 = 9*

Dividing both sides by 9, we get:

* = 52/9

Simplifying further, we get:

* = 5.7778

Therefore, the value of * is 6 (approximate to one decimal place).

Hence, the correct option is (a) 6.

If A:B=3:2 and B:C=3:5, then A:B:C is
  • a)
    9:6:10
  • b)
    6:9:10
  • c)
    10:9:6
  • d)
    none of these
Correct answer is option 'A'. Can you explain this answer?

Nandini Iyer answered
A:B = 3:2 
B=2 when A=3 

B:C = 3:5 
B=3 when C=5 

But to connect the two ratios you need B to be the same number in both. Find the Least Common Multiple. 
LCM(2, 3) = 6 

Now scale the equations so that B becomes 6. 
A:B = 3:2 = 9:6 
B:C = 3:5 = 6:10 

A:B:C = 9:6:10

The fourth proportional to 4, 6, 8 is
  • a)
    12
  • b)
    32
  • c)
    48
  • d)
    none of these
Correct answer is option 'A'. Can you explain this answer?

Manoj Ghosh answered
For proportions; the product of the internal terms equals the product of the externals.
Therefore,

=> 4 : 8 = 6: x
=> 4x = 48
=> x = 12.

So, the answer is 12.

If loga b + loga c=0 then
  • a)
    b=c
  • b)
    b=-c
  • c)
    b=c=1
  • d)
    b and c are reciprocals.
Correct answer is option 'D'. Can you explain this answer?

Srsps answered
Given the equation:
loga b + loga c = 0
Step 1: Apply the logarithmic sum property
The sum of two logarithms with the same base can be combined:
loga b + loga c = loga (b ⋅ c)
So the equation becomes:
loga (b ⋅ c) = 0
Step 2: Understand the meaning of loga x = 0
From logarithmic properties, we know that:
loga x = 0 implies x = a0
And since a0 = 1, we get:
x = 1
Step 3: Apply this to b ⋅ c
From loga (b ⋅ c) = 0, we conclude:
b ⋅ c = 1
Final Result:
If loga b + loga c = 0, then:
b ⋅ c = 1

If p/q =r/s=2.5/1.5, the value of ps:qr is
  • a)
    3/5
  • b)
    1:1
  • c)
    5/3
  • d)
    none of these
Correct answer is option 'B'. Can you explain this answer?

Dhruv Mehra answered
p/q =r/s

=> ps =qr {cross multiplication }

putting the value

2.5 X 1.5 =2.5 X 1.5

=> 1 =1

therefore, we get ps :qr=1:1

Chapter doubts & questions for Chapter 1: Ratio and Proportion, Indices, Logarithms - Quantitative Aptitude for CA Foundation 2025 is part of CA Foundation exam preparation. The chapters have been prepared according to the CA Foundation exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for CA Foundation 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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