CA Foundation Maths solutions Exercise 1A

Chapter 1 Ratio and Proportions, Indices, Logarithms Exercise 1A C.A. foundation maths solutions are given.

Basic problems and solutions for Ratios and Proportions are also given.

You should study the textbook lesson chapter 1 very well.

You should also practice all example problems and solutions which are given in the textbook.

CA foundation maths solutions

Ratio and Proportions, Indices, Logarithms

Important points

Chapter 1 Exercise 1A Ratios C.A. foundation maths solutions

C.A. Foundation maths solutions

Chapter 1

Ratio and proportion, Indices, logarithms

Ratios

Exercise 1(A)

Problem 1

The inverse ratio of 11:15 is

Solution:

We know that the inverse of a : b is b : a. Hence inverse ratio of 11:15 is 15 : 11.

Problem 2

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

Solution:

We know that 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.

It is given that the antecedent is 15

15/x = 3/4 , x = (15× 4)/3 = 60/ 3 = 20

Hence the consequent, x = 20

Problem 3

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

Solution:

The ratio of the quantities 5 : 7, the inverse of it will be 7 : 5

Let antecedent be x.

It is given that the consequent of its inverse ratio is 5.

x/5 = 7/5 , x = (7×5)/5 = 7

Hence the antecedent, x = 7

Problem 4

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

We know that the compounded ratio of given ratios is the multiplication of given ratios.

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

(2/3) × (9/4) × (5/6) × (8/10) = 720/720 = 1/1

So,the ratio compounded of 2:3, 9:4, 5:6 and 8:10 is 1 : 1

Problem 5

The duplicate ratio of 3:4 is

Solution:

We know that the duplicate ratio is the compound ratio of itself. The ratio is multiplied by itself to get duplicate ratio.

The duplicate ratio of 3:4 will be square of (3:4) = 9:16.

Problem 6

The sub duplicate ratio of 25:36 is

Solution:

We know that the sub duplicate ratio of a:b is √a:√b.

Hans the sub duplicate ratio of 25 : 36 is 5:6.

Problem 7

The triplicate ratio of 2:3 is

Solution:

We know that the triplicate ratio is cube of the given ratio.

Hence the triplicate ratio of 2:3 is 8:27.

Problem 8

The sub triplicate ratio of 8:27 is

Solution:

We know that the sub triplicate ratio of a:b is cube root of a : cube root of b

Hence the sub triplicate ratio of 8:27 is 2:3.

Problem 9

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

Solution:

The duplicate ratio of 3:4 is 9:16
Hence the ratio compounded of 4:9 and 9:16 is

(4/9) × (9/16) = 4/16 = 1/4 = 1:4

Problem 10

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

Solution:

We know that the compounded ratio of given ratios is the multiplication of given ratios.

The duplicate ratio of 3 : 4 is 9 : 16

The triplicate ratio of 2 : 3 is 8 : 27

Hence the ratio compounded of 4:9, 9:16, 8:27 and 9:7 is

4/9 × 9/16 × 8/27 × 9/7 = 2/21= 2 : 21

So,the ratio compounded of 2:3, 9:4, 5:6 and 8:10 is 2 : 21

Problem 11

The ratio compounded of duplicate ratio of 4 : 5, triplicate ratio of 1 : 3, sub duplicate ratio of 18 : 256 and sub triplicate ratio of 125 : 512 is

Problem 12

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

Problem 13

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

Problem 14

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

Problem 15

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

Problem 16

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

Problem 17

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

Problem 18

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

Problem 19

If x : y = 3:4, the value of x²y + xy² : x cube + y cube is

Problem 20

If p : q is the sub duplicate ratio of p – x² : q – x² then x² is

Problem 21

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

Problem 22

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

Problem 23

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

Problem 24

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