### RATIO and PROPORTION Problem with Solutions

For all competitive exams Ratio and Proportion is an important chapter. Ratio and Proportion chapter at least 2-3 problems are appear in all competitive exams like SSC and bank exams (SBI and IBPS-clerk and PO). This section will teach you to understand Ratio and Proportion problems with explanation and short cut to solve problems quickly.

**Ratio and Proportion – Study material for all competitive exams**

Ratio and Proportion is a part of quantitative or numerical aptitude section for all competitive exams. This chapter will give brief explanation to Ratio and Proportion Problems. This will be very helpful to crack all competitive exams with more marks. “Practice makes a man perfect” so please practice more problems with different models. All the best for your preparations and success.

#### Important formulas for Ratio and Proportion:

*Ratio means the number of times one quantity contains another quantity. However, the quantities in question should be of same type.*

Ratio is expressed in the format A:B or A/B.

In A:B, A is called antecedent and B is called consequent.

#### Types of Ratio:

**Duplicate Ratio:**This ratio is the square of two numbers. Example: 25:4 is the duplicate ratio of 5:2.**Triplicate Ratio:**This ratio is the cube of two numbers. Example: 125:8 is the triplicate ratio of 5:2.**Sub-duplicate Ratio:**This ratio is the square root of two numbers. Example: 5:2 is the sub-duplicate of 25:4**Sub-triplicate Ratio:**This ratio is the cube root of two numbers. Example: 5:2 is the sub-duplicate of 125:8**Inverse Ratio:**The ratio in which antecedent and consequent change their places. Example: 25:4 is the inverse of 4:25.

*Two ratios are said to be in Proportion when they are equal. *

** For example:** 2/5 = 4/10.

This is because 4/10 can be divided by 2 and can be simplified as 2/5. Hence, 2/5 and 4/10 are said to be in proportion. In the equation A:B = C:D, A and D are called

*extremes*, whereas B and C are called

*means*.

In a proportion, *product of means is always equal to product of extremes.*

In other words, for proportion A:B = C:D;

*AD = BC*

#### Types of Proportions:

**Forth Proportion:**When a:b = c:d, then d is called the forth proportion of a,b and c.**Third Proportion:**When a:b = b:c, then c is called the third proportion of a and b.**Second Proportion:**When a:b = b:c, then b is called second or mean proportion of a and c.

#### Shortcut tricks:

**Shortcut 1: **When A : B = m : n, and B : C = p : q. Then A : B : C = mp : pn :nq

**Shortcut 2: **When A : B = m : n, B : C = p : q, and C : D = r : s. Then A : B : C : D = mpr: npr : nqr : nqs

**Shortcut 3: **In a container, the ratio between oil and water is P:Q. The total quantity is x litres. To find the amount of water to be mixed so that the ratio becomes A:B, use

x(pb – qa)/a(p + q)

Let us see problems with explanation.

### RATIO and PROPORTION Problem with Solutions

Before go through the problems of Ratio and Proportion. Please understand and learn basic formulas of Ratio and Proportion.

Complexity of the question is differ for each exams. While learning solve high difficulty questions to boost your knowledge and success your exams.

**1) A bucket contains a mixture of two liquids A & B in the proportion 5 : 3. If 16 litres of the mixture is replaced by 16 litres of liquid B, then the ratio of the two liquids becomes 3 : 5. How much of the liquid B was there in the bucket?**

** A) 16.5 l**

** B) 18 l**

** C) 14.5 l**

** D) 15 l**

** E) None**

**Explanation:**

Let bucket contains 5x and 3x of liquids A and B respectively.

When 16 litres of mixture is replaced, A and B has a mixture is

[5x – (5/8)*16] = (5x – 10)

[3x – (3/8)*16] = (3x – 6)

Ratio (5x – 10)/(3x – 6+16) = 3/5

(5x – 10)/(3x +10) = 3/5

X=5.

So, quantity of liquid B initially,

= 3*5 = 15 litres.

**2) The difference between two positive numbers is 10 and the ratio between them is 5:3. Find the product the two numbers**

** A) 360**

** B) 375**

** C) 390**

** D) 425**

** E) None**

**Explanation: **

Let the two positive numbers be 5x and 3x respectively.

5x-3x = 10

x = 5.

Then numbers are 25 and 15.

Thus, their product = 25*15 = 375.

**3) If the ratio of the ages of Guna and Shekar is 6:7 at present, and twelve years from now, the ratio will get changed to 8:9, then find Guna’s present age.**

** A) 38**

** B) 46**

** C) 42**

** D) 36**

** E) None**

Explanation:

Explanation:

Let Guna’s and Shekar’s present age is 6x and 5x respectively.

then

(6x+12)/(7x+12) = 8/9

54x+108 = 56x + 96

2x = 12

x = 6

Present age of Guna = 6x = 36.

**4) The ratio of Elephant and Deer in the zoo is 43 : 47 respectively. The average number of Elephant and Deer in the zoo is 135. What is the number of Deer in the pond ?**

** A) 166**

** B) 135**

** C) 141**

** D) 156**

** E) None**

**Explanation:**

Ratio 43:47

Average 135

Then Total=2*135=270.

Deer=270*47/90

=141.

**5) The ratio of male and female in a city is 7 : 8 respectively and percentage of children among male and female is 25 and 20 respectively. If number of adult females is 156800, what is the total population of the city?**

** A) 400000**

** B) 386400**

** C) 367500**

** D) 412300**

** E) None**

**Explanation:**

Let the total population be ‘p’

Male :Female 7 : 8

Percentage of children among male and female is 25% and 20%

Then Adults male and female % = 75% & 80%

=> 80%(8p/15) = 156800

=> 80 x 8p/15 x 100 = 156800

=> p = 156800 x 15 x 100/80 x 8

=> p = 367500

Therefore, the total population of the city = p = 367500.

**6) If 8 men and 3 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a boy and that of a man for a given time ?**

** A) 2:3**

** B) 3:2**

** C) 4:1**

** D) 1:4**

** E) None**

**Explanation:**

8M+3B=4(1M+1B)

8M+3B=4M+4B

4M=B

B:M=4:1

**7) In a competitive exam, the number of passed students was four times the number of failed students. If there had been 35 fewer appeared students and 9 more had failed, the ratio of passed and failed students would have been 2 : 1, then the total number of students appeared for the exam ?**

** A) 170**

** B) 165**

** C) 180**

** D) 155**

** E) None**

**Explanation:**

Let the number of failed students be x

Number of passed students = 4x

So total number of students was 5x

From the given data

If total number of students be 5x – 35

(5x-35)/x+9=3/1

x = 31

Total number = 31×5 = 155

**8) There are two container of equal capacity . The ratio of milk to water in 1st can 5:3 and in 2nd can is 4:3. If they are mixed up, what is the new ratio?**

** A) 45:67**

** B) 55:68**

** C) 67:45**

** D) 37:45**

** E) None**

**Explanation:**

Two can has equal capacity. So we consider 10litre in each can.

1st can (5+3) 8 10

Milk 5 ===> 25/4L

Water 3 ===>15/4L

2nd can (4+3) 7 10

Milk 4 ===> 40/7L

Water 3 ===>30/7L

Then New ratio

M+M 25/4 +40/7 : W+W 15/4+30/7

335/28: 225/28=67:45

**9) A child has 3 different kinds of chocolates costing Rs 2, Rs 5 and Rs 10. He spends a total Rs. 140 on the chocolates. How many chocolate minimum and maximum we can buy with one condition we must buy from all varieties?**

** A) 19, 63**

** B) 20, 60**

** C) 22, 62**

** D) 17, 56**

** E) None**

**Explanation: **

To buy maximum chocolates we must buy Rs 2 choclate more.

10*1=10

5*2=10(we can’t buy one chocolate from Rs 5 because we have amount in even no )

2*60=120

Total chocolate (1+2+60)=63.

To buy minimum chocolates we must buy Rs 10 choclate more.

2*5=10

5*2=10(we can’t buy one chocolate from Rs 5 because we have amount in even no )

10*12=120

Total chocolate (5+2+12)=19.

**10) Rs. 1278 is divided among 6 men, 5 women and 3 boys. The ratio of share of a man, a woman and a boy is 8: 11: 13. What is the share of a man?**

** A) Rs85**

** B) Rs72**

** C) Rs90**

** D) Rs110**

** E) None**

**Explanation: **

Ratio 8:11:13

No of men, women and boys are 6, 5, 3

Then ratio of men, women and boys 6*8 : 5*11 : 13*3

=48:55:39

Men part is= (48/142)* 1278 = 432

Then 1 man part= 432/6 =72