PRACTICE QUESTIONS ON RATIO INDICES AND LOGARITHMS CA FOUNDATION

Problem 1 :

If 10% of x = 20% of y, then x : y is equal to 

(a) 1 : 2     (b) 2 : 1      (c) 5 : 1        (d) 10 : 1

Solution:

So, option (b) is correct.

Problem 2 :

(a) 23         (b) 20         (c) 1            (d) 8

Solution:

So, option (d) is correct.

Problem 3 :

A person has assets worth Rs. 1,48,200. He wish to divide it amoungst his wife, son and daughter in the ratio 3 : 2 : 1 respectively. From this assets the share of his son will be 

(a) Rs. 74,100         (b) Rs. 37,050       (c) Rs. 49,400

(d) Rs. 24,700

Solution:

Asset = Rs.148200

Let the ratio be 3x : 2x : x

3x + 2x + x = 148200

6x = 148200

x = 148200/6

x = 24700

Share of son = 2x 

= 2 × 24700

= Rs. 49400

So, option (c) is correct.

Problem 4 :

Which of the following is true?

Solution:

So, option (a) is correct.

Problem 5 : 

Rs.407 are to be divided among A, B and C so that their shares are in the ratio 1/4 : 1/5 : 1/6. The respective shares of A, B, C are:

(a) Rs.165, Rs.132, Rs.110        (b) Rs.165, Rs.110, Rs.132

(c) Rs.132, Rs.110, Rs.165        (d) Rs.110, Rs.132, Rs.165

Solution:

Multiplying both sides by 60, we get

Let the amount of A, B, and C be 15x, 12x, and 10x.

15x + 12x + 10x = 407

37x = 407

x = 407/37

x = 11

A = 15 × 11 = Rs. 165

B = 12 × 11 = Rs. 132

C = 10 × 11 = Rs. 110

So, option (a) is correct.

Problem 6 :

If log_xY = 100 and log₂x = 10, then the value of 'Y' is :

(a) 2¹⁰        (b) 2¹⁰⁰             (c) 2^1,000                (d) 2^10,000

Solution:

log₂x = 10

x = 2¹⁰

log_xY = 100

Y = x¹⁰⁰

Y = (2¹⁰)

Y = 2¹⁰⁰⁰

So, option (C) is correct.

Problem 7 :

Which of the numbers are not in proportion?

(a) 6, 8, 5, 7                (b) 7, 14, 16, 32

(c) 18, 27, 12, 18        (d) 8, 6, 12, 9

Solution:

So, option (a) is correct.

Problem 8 :

If a = 5^1/3 + 5^-1/3, then the value of 5a³ - 15a is equal to 

(a) 25        (b) 26        (c) 27           (d) 28

Solution:

So, option (b) is correct.

Problem 9 :

If A : B = 8 : 15, B : C = 5 : 8 and C : D = 4 : 5, then A : D is equal to

(a) 2 : 7         (b) 4 : 15          (c) 8 : 15         (d) 15 : 4

Solution:

So, option (b) is correct.

Problem 10 :

log(25/4) is equal to

(a) log 25/log 4      (b) log 25 - log 4     (c) 25/4

(d) none of these

Solution:

So, option (b) is correct.