# 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.

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**

**Problem 25
**

**The ratio between the speeds of two trains is 7:8, If the second train runs 400 kms. in 5 hours, the speed of the first train is**

**Some more problems for CA Foundation maths solutions **

Find the compounded ratio of 4:5, 5:7 and 9:11

Find the duplicate ratio of √5 : 7

Find the triplicate ratio of 3:4

Find the sub triplicate ratio of 9:16

Find the triplicate ratio of 1 cube : 2 cube.

Find the reciprocal ratio of 4:7

Find the triplicate ratio of 1/2 : 1/3.

Simplify the ratio 1/3:1/8 :1/6.

Find the reciprocal ratio of 3 square : 4 square.

Find the sub triplicate ratio of 27a cube : 64b cube.

Find the reciprocal ratio of 3 square : 4 square.

Find the sub triplicate ratio of 1/8 : 1/125.

Find the sub duplicate ratio of 9:16.

Find the triplicate ratio of 1^3:2^3

Find the triplicate ratio of 1/ 2 : 1/3.

A fraction bears the same ratio to 1/27 as 3/7 does to 5/9. What is the fraction?

Find the compounded ratio of 2:3 and 4:9.

### CA foundation maths solutions for Ratio and Proportions

Length and a breadth of a rectangular field are 50 m and 15 m respectively. Find the ratio of the length to the breadth of the field.

An alloy consist of 27 1/2 kg of copper and 2 3/4 kg of tin. Find the ratio by weight of tin to the alloy.

The sub triplicate ratio of 8 : 27 is.

If 2x + 3 : 5x – 8 be the duplicate ratio of √5 : √6 then the value of x is

Note : You should observe the solutions. You will be try them in your own method.

SSC Maths textbook Solutions class 10

Inter Maths 1A Solutions textbook

Inter Maths 1B textbook solutions

Inter Maths 1IA text book solutions

Inter Maths IIB text book solutions

NCERT maths class 8 solutions for some chapters