PRACTICE QUESTIONS ON RATIO AND PROPORTION FOR CA FOUNDATION

Problem 1 :

(a) invertendo  (b) componendo        (c) dividend

(d) alternendo

Solution:

This is alternendo property of proportion.

Problem 2 :

If the salary of P is 25% lower than that of Q and salary of R is 20% highest than that of Q the ratio of the salary of R and P will be.

(a) 5 : 8     (b) 5 : 3         (c) 8 : 5        (d) 3 : 5

Solution:

Let x be Q's income.

Salary of P = 75% of Q

Salary of R = 120% of Q

Ratio between R to P :

= (120Q/100) : (75Q/100)

= 120Q : 75Q

= 8 : 5

Problem 3 :

log_(1/5) 625 = 

(a) 4      (b) -4       (c) 25     (d) -25

Solution:

So, option (b) is correct.

Problem 4 :

If x = 1 + √2, then (1 + x)(1 - x) is equal to

(a) -2 - 2√2     (b) 2 + √2       (c) 2 + 2√2         (d) 2 - 2√2

Solution:

x = 1 + √2

(1 + x)(1 - x) = (1 + (1 + √2))(1 - (1 + √2))

= (1 + 1 + √2)(1 - 1 - √2)

= -√2(2 + √2)

= -2√2 - 2

So, option (a) is correct.

Problem 5 :

The third proportional to 49 and 21 is

(a) 49        (b) 21          (c) 9           (d) 3

Solution:

Where, C = third proportional

A = first proportional

B =  second proportional

So, option (c) is correct.

Problem 6 :

(a) 0           (b) 1          (c) -1        (d) None

Solution:

So, option (b) is correct.

Problem 7 :

Find the value of : [1 - {1 - (1 - x²)^-1}^-1]^-1/2 

(a) 1/x         (b) x            (c) 1          (d) none of these

Solution:

So, option (b) is correct.

Problem 8 :

4, *, 9, 13 1/2 are in proportion. Then * is

(a) 6            (b) 8               (c) 9           (d) none of these

Solution:

So, option (a) is correct.

Problem 9 :

The value of log₆6 is

(a) 0           (b) 1              (c) 2         (d) none of these

Solution:

We use the definition of logs

log_ab = c

a^c = b

log₆6 = c

6^c = 6

c = 1

log₆6 = 1

So, option (b) is correct.

Problem 10 :

(a) 9           (b) 1/9          (c) 1       (d) none of these

So, option (d) is correct.