Ratio and Proportion

1.Find a fourth proportional to the numbers 6, 8, 9. 

a) 12

b) 7

c) 5

d) 14

2.Find the value of the missing figure in the question given below. 

6 : ? :: 5 : 35

a) 30

b) 36

c) 42

d) 48

3.Find a fourth proportional to the numbers 12, 14, 24. 

a) 38

b) 36

c) 28

d) 30

4.If 15 books cost Rs. 35, what do 21 books cost? 

a) Rs.28

b) Rs.49

c) Rs.52

d) Rs.40

5.If 15 men can reap a field in 28 days, in how many days will 5 men reap it?

a) 78 days

b) 66 days

c) 84 days

d) 94 days

6.A fort hand provisions for 150 men for 45 days. After 10 days, 25 men left the fort. How long will the food last at the same rate for the remaining men? 

a) 42 days 

b) 45 days

c) 55 days

d) 38 days

7.If 18 men can reap 80 hectares in 24 days, how many hectares can 36 men reap in 30 days.

a) 240 hectares.

b) 450 hectares.

c) 320 hectares.

d) 360 hectares.

8.If 30 men do a piece of work in 27 days, in what time can 18 men do another piece of work 3 times as great? 

a) 145 days

b) 135 days

c) 130 days

d) 134 days 

9.If the carriage of 810 kg for 70 km cost Rs. 112.50, what will be the cost of the carriage of 840 kg for a distance of 63 km at half the former rate? 

a) Rs. 52

b) Rs. 53

c) Rs. 521/2

d) Rs. 501/4

10.If 300 men could do a piece of work in 16 days, how many men would do 1/4 of the same work in 15 days?

a) 80 men

b) 85 men

c) 90 men

d) 75 men 

Answers :
 1. a
 2. c
 3. c
 4. b
 5. c
 6. a
 7. b
 8. b
 9. c
10.a

Ratio and Proportion

1.Two alloys A and B contain gold and silver in the ratio of 1 : 2 and 1 : 3 respectively. A third alloy C is formed by mixing A and B in the ratio of 2 : 3. Find the percentage of silver in the alloy C.

(a) 71 2/3%

(b) 28 1/3%

(c) 70 2/3%

(d) 29 1/3%

1. A

(Solution)

Alloy A = 300 and B = 300

Let 100 : 200 ( 1 : 2)

75 : 225 (1 : 3) 

A = 100 × 2 : 200 × 2

75 × 3 : 225 × 3

425 : 1075 

For % =1075/1500×100=215/3=71(2/3%)

2.Two alloy contain silver and copper in the ratio of 2 : 3 and 3 : 4. In what ratio the two alloys should be added together to get a new alloy having silver and copper in the ratio of 1 : 2? Find the percentage of gold in the alloy C.

(a) 41 19/21% 

(b) 67 13/21%

(c) 32 5/21

(d) 67 16/21%

2.A (Same as question 1)

3.An amount of Rs. 1250 is distributed among A, B and C in the ratio of 4 : 7 : 14. What is the ratio between the difference of shares of B and A and the difference of shares of C and B ?

(a) 7 : 3 

(b) 2 : 7 

(c) 3 : 7 

(d) 7 : 2 

3.C

4.The prices of a scooter and a television set are in the ratio 3 : 2. If a scooter costs Rs. 6000more than the television set, the price of the television set is:

(a) Rs. 18000 

(b) Rs. 12000

(c) Rs. 10000

(d) Rs. 6000

4.B 

5.The contents of two vessels containing water and milk are in the ratio 3 : 4 and 5 : 4 are mixed in the ratio 1 : 4. The resulting mixture will have water and milk in the ratio_________.

(a) 184 : 176 

(b) 167 : 184

(c) 167 : 148

(d) 148. 167

5.C

6.The contents of two vessels containing water and milk are in the ratio 2 : 3 and 4 : 5 are mixed in the ratio 1 : 2. The resulting mixture will have water and milk in the ratio_________.

(a) 77 : 58 

(b) 58 : 77

(c) 68 : 77

(d) 77 : 68  

6.B

7.The contents of two vessels containing water and milk are in the ratio 1 : 2 and 2 : 5 are mixed in the ratio 1 : 4. The resulting mixture will have water and milk in the ratio _________.

(a)  31:74

(b)  31:77

(c)  33:74

(d)  33:76

7. A

Solutions 

Detail Method: Change the ratios into fractions.

Water       :  Milk

Vessel I  1/3    2/3

Vessel II 2/7 5/7

From Vessel I, I/5 is taken and from Vessel II,  4/5 is taken.

Therefore, the ratio of water to milk in the new vessel =(1/3×1/5+2/7×4/5):(2/3×1/5+5/7×4/7)  

=(1/15+8/35):(2/15+20/35)=31/105:74/105=31∶74  

Quicker Method: Applying the above theorem, we have, 

The required answer = 1×1×(2+5)+4×2(1+2) ∶1×2(2+5)+4×5(1+2)

=1×7+8×3∶2×7+20×3=31∶74 

8.Two vessels contain equal quantity of mixtures of milk and water in the ratio 5 : 2 and 6 : 1 respectively. Both the mixtures are now mixed thoroughly. Find the ratio of milk to water in the new mixture so obtained. 

(a)  11:3

(b) 3:11

(c) 12:4

(d) 5:12

8. A

9.One man adds 3 litres of water to 12 litres of milk and another 4 litres of water to 10 litres of milk. What is the ratio of the strengths of milk in the two mixtures?

(a)  27:26

(b) 24:25

(c) 28:25

(d) 25:45

9. C

Solution

Strength of milk in the mixture =(Quantity of Milk)/(Total Quantity of Mixture)

∴ Strength of milk in the first mixture =12/(12+3)=12/15

Strength of milk in the second mixture= 10/(10+4)=10/14

∴ The ratio of their strengths =12/15:10/14

=12×14∶15 ×10  

=28∶25  

10.A bag contains rupee, 50-paise and 25-paise coins in the ratio 3 : 4 : 5. If the total amount in the bag is Rs. 625, find the no. of coins of 25-paise. 

(a) 125 

(b) 1250

(c) 500

(d) 1000

10. C

Ratio and Proportion

Ratio And Proportion

What is Ratio?

Ratio is a mathematical term used to compare two similar quantities expressed in the same units. The ratio of two terms ‘x’ and ‘y’ is denoted by x : y. In ratio x : y , we can say that x as the first term or antecedent and y, the second term or consequent.

In general, the ratio of a number x to a number y is defined as the quotient of the numbers x and y i.e. x/y. 

Example: The ratio of 25 km to 100 km is 25:100 or 25/100, which is 1:4 or 1/4, where 1 is called the antecedent and 4 the consequent.

Note that fractions and ratios are same; the only difference is that ratio is a unit less quantity while fraction is not. 

Compound Ratio

Ratios are compounded by multiplying together the fractions, which denote them; or by multiplying together the antecedents for a new antecedent, and the consequents for a new consequent. The compound of a : b and c : d is  i.e. ac : bd. 

Properties of Ratio:

☑ a : b = ma : mb, where m is a constant

☑ a : b : c = A : B : C is equivalent to a / A = b /B = c /C, this is an important property and has to be used in ratio of three things.

☑

i.e. the inverse ratios of two equal ratios are equal. This property is called Invertendo. 

☑ 

i.e. the ratio of antecedents and consequents of two equal ratios are equal. This property is called Alternendo.

☑ 

This property is called Componendo.

☑  

This property is called Dividendo. 

☑ 

This property is called Componendo - Dividendo. 

☑
 
☑The incomes of two persons are in the ratio of a: b and their expenditures are in the ratio of c: d. If the saving of each person be Rs. S, then their incomes are given by-

Example: Annual income of A and B are in the ratio of 5: 4  and their annual expenses bear a ratio of 4: 3. If each of  them saves Rs. 500 at the end of the year, then find the  annual income. 

Dividing a Quantity Into a Ratio

Suppose any given quantity ‘a’ is to be divided in the ratio of m : n. 

Then, 

Proportion

When two ratios are equal, the four quantities composing them are said to be in proportion. 

If a/b=c/d, then a, b, c, d are in proportions. 

This is expressed by saying that ‘a’ is to ‘b’ is to ‘c’ is to ‘d’ and the proportion is written as 

a : b :: c : d or a : b = c : d 

(product of means = product of extremes)

If there is given three quantities like a, b, c of same kind then we can say it proportion of continued.

a : b = b : c the middle number b is called mean proportion. a and c are called extreme numbers.

So, b² = ac. (middle number)² = ( First number x Last number ).

Application: These properties have to be used with quick mental calculations; one has to see a ratio and quickly get to results with mental calculations.

Example: 

 should quickly tell us that 

Q. A certain amount was to be distributed among A, B and C in the ratio 2 : 3 : 4, but was erroneously distributed in the ratio 7 : 2 : 5. As a result of this, B received Rs. 40 less. What is the actual amount? 

(a) Rs. 210

(b) Rs. 270

(c) Rs. 230

(d) Rs. 280

(e) None of these

Q. Mixture of milk and water has been kept in two separate containers. Ratio of milk to water in one of the containers is 5 : 1 and that in the other container 7 : 2. In what ratio the mixtures of these two containers should be added together so that the quantity of milk in the new mixture may become 80%? 

(a) 2 : 3

(b) 3 : 2

(c) 4 : 5 

(d) 1 : 3 

 (e) None of these

Ratio and proportion

Ratio And Proportion

What is Ratio?

Ratio is a mathematical term used to compare two similar quantities expressed in the same units. The ratio of two terms ‘x’ and ‘y’ is denoted by x : y. In ratio x : y , we can say that x as the first term or antecedent and y, the second term or consequent.

In general, the ratio of a number x to a number y is defined as the quotient of the numbers x and y i.e. x/y. 

Example: The ratio of 25 km to 100 km is 25:100 or 25/100, which is 1:4 or 1/4, where 1 is called the antecedent and 4 the consequent.

Note that fractions and ratios are same; the only difference is that ratio is a unit less quantity while fraction is not. 

Compound Ratio

Ratios are compounded by multiplying together the fractions, which denote them; or by multiplying together the antecedents for a new antecedent, and the consequents for a new consequent. The compound of a : b and c : d is  i.e. ac : bd. 

Properties of Ratio:

☑ a : b = ma : mb, where m is a constant

☑ a : b : c = A : B : C is equivalent to a / A = b /B = c /C, this is an important property and has to be used in ratio of three things.

☑

i.e. the inverse ratios of two equal ratios are equal. This property is called Invertendo. 

☑ 

i.e. the ratio of antecedents and consequents of two equal ratios are equal. This property is called Alternendo.

☑ 

This property is called Componendo.

☑  

This property is called Dividendo. 

☑ 

This property is called Componendo - Dividendo. 

☑
 
☑The incomes of two persons are in the ratio of a: b and  their expenditures are in the ratio of c: d. If the saving of each person be Rs. S, then their incomes are given by-

Example: Annual income of A and B are in the ratio of 5: 4  and their annual expenses bear a ratio of 4: 3. If each of  them saves Rs. 500 at the end of the year, then find the  annual income. 

Dividing a Quantity Into a Ratio

Suppose any given quantity ‘a’ is to be divided in the ratio of m : n. 

Then, 

Proportion

When two ratios are equal, the four quantities composing them are said to be in proportion. 

If a/b=c/d, then a, b, c, d are in proportions. 

This is expressed by saying that ‘a’ is to ‘b’ is to ‘c’ is to ‘d’ and the proportion is written as 

a : b :: c : d or a : b = c : d 

(product of means = product of extremes)

If there is given three quantities like a, b, c of same kind then we can say it proportion of continued.

a : b = b : c the middle number b is called mean proportion. a and c are called extreme numbers.

So, b² = ac. (middle number)² = ( First number x Last number ).

Application: These properties have to be used with quick mental calculations; one has to see a ratio and quickly get to results with mental calculations.

Example: 

 should quickly tell us that 

Q. A certain amount was to be distributed among A, B and C in the ratio 2 : 3 : 4, but was erroneously distributed in the ratio 7 : 2 : 5. As a result of this, B received Rs. 40 less. What is the actual amount? 

(a) Rs. 210

(b) Rs. 270

(c) Rs. 230

(d) Rs. 280

(e) None of these

Q. Mixture of milk and water has been kept in two separate containers. Ratio of milk to water in one of the containers is 5 : 1 and that in the other container 7 : 2. In what ratio the mixtures of these two containers should be added together so that the quantity of milk in the new mixture may become 80%? 

(a) 2 : 3

(b) 3 : 2

(c) 4 : 5 

(d) 1 : 3 

 (e) None of these

Ratio and Proportion

Dear students,
Now you have checked scores and start preparing for the Tier -II . we are going to provide Quant quizzes specifically for the mains exam . 

Now, we're going to provide Short Tricks with Example Questions, So that you can familiarise yourself with tricky scenarios of Quant. Every day we'll post Some useful Tricks for SSC CGL Tier -II, and it will help you in scoring respected marks.

                                 

                               Percentage wise distribution of Topics For Tier-II                                          

Ratio and Proportion 

Concept And Tricks Of Ratio And Proportion

Concept And Tricks Of Ratio And Proportion

What is Ratio?

A ratio is a relationship between two numbers by division of the same kind. The ration of a to b is written as a : b = a / b In ratio a : b , we can say that a as the first term or antecedent and b, the second term or consequent.

Example :  The ratio 4 : 9 we can represent as  4 / 9 after this 4 is a antecedent and , consequent = 9

Rule of ration :  In ratio multiplication or division of each and every term of a ratio by the same non- zero number does not affect the ratio.

Different type of ratio problem is given in Quantitative Aptitude which is a very essential topic in competitive exam. Under below given some more example for your better practice.

Anything we learn in our school days was basics and that is well enough for passing our school exams. Now the time has come to learn for our competitive exams. For this we need our basics but also we have to learn something new. That’s where shortcut tricks and formula are comes into action.

What is Proportion?

The idea of proportions is that two ratio are equal.

If a : b = c : d, we write a : b : : c : d,

Ex. 3 / 15 = 1 / 5

a and d called extremes, where as b and c called mean terms.

Proportion of quantities

the four quantities a, b, c, d said proportion then we can express it

a : b = c : d

Then a : b : : c : d  <–> ( a x d ) = ( b x c )

product of means = product of extremes.

If there is given three quantities like a, b, c of same kind then then we can say it proportion of continued.

a : b = b : c the middle number b is called mean proportion. a and c are called extreme numbers.

So, b^2 = ac. ( middle number )^2 = ( First number x Last number ).