# Ratio and Proportion Questions and Answers

## Ratio and Proportion Questions

Ratio and Proportion Questions and Answers are given on this page for students to practice and get an idea how this topic is asked in the exam. ### Some of the major formulas  are as follows:-

• The ratio of two people a and b is denoted as a : b.
• a : b = ma : mb, where m is a constant.
• x : y : z = X : Y : Z is equivalent to x/X=y/Y=z/Z
• If x/y = z/a  then, x+y/x-y  = z+a/z-a

### Key points :-

• Ratios compare two or more quantities.
• Proportions are equations that state two ratios are equal.
• You can solve for unknown values in proportions using cross-multiplication.

## Practice Ratio and Proportion Questions and Answers

1. The salaries of A, B, and C are in the ratio of 1 : 2 : 3. The salary of B and C together is Rs. 6000. By what percent is the salary of C more than that of A? 300%

300%

44.09%

200%

200%

41.94%

400%

400%

5.38%

600%

600%

8.6%

Let the salaries of A, B, C be x, 2x and 3x respectively.

Then,2x + 3x = 6000 => x = 1200.

A's salary = Rs. 1200, B's salary = Rs. 2400, and Cs salary Rs. 3600.
Excess of C's salary over A's=$\frac{2400}{1200}\times 100$= 200%. 2. A sum of Rs. 427 is to be divided among A, B and C such that 3 times A’s share, 4 tunes B’s share and 7 times C’s share are all equal. The share of C is : 196

196

18.64%

84

84

55.93%

120

120

11.86%

165

165

13.56%

3A = 4B = 7C = k,Then A = k/3, B = k/4 and C= k/7.

A : B : C = k/3 : k/4 : k/7 = 28:21 :12.

Cs share = Rs. [427 x (12/61)] = Rs. 84 3. In a zoo, there are rabbits and pigeons. If heads are counted, there are 340 heads and if legs are counted there are 1060 legs.How many pigeons are there? 150

150

50%

160

160

9.38%

180

180

14.06%

190

190

26.56%

Suppose there are all the pigeons then total no of heads are 340 and total no of legs are 1060. Let us suppose number of rabbits is x and number of pigeons is y.
We know rabbit has 4 legs and pigeon has 2.
so, 1st equation will be x + y = 340
and, 2nd equation will be 4x + 2y = 1060.
solving, 1st and 2nd equation we get number of pigeons = 150 4. Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps? 25:2

25:2

82.09%

24:3

24:3

10.45%

22:1

22:1

4.48%

22:4

22:4

2.99%

Indian stamps are common to both ratios. Multiply both ratios by factors such that the Indian stamps are represented by the same number.

US : Indian = 5 : 2, and Indian : British = 5 : 1. Multiply the first by 5, and the second by 2.

Now US : Indian = 25 : 10, and Indian : British = 10 : 2

Hence the two ratios can be combined and US : British = 25 : 2

Video solution: 5. A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is : 8:4

8:4

12.96%

9:5

9:5

72.22%

9:4

9:4

9.26%

9:7

9:7

5.56%

Dog : Hare = (3*3) leaps of hare : 5 leaps of hare = 9 : 5. 6. In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is 550

550

8.06%

416

416

79.03%

300

300

4.84%

200

200

8.06%

Let the number of boys and girls be 8x and 5x.
As we know number of girls is 160.
We even know 5x is the ratio of girls in the college.
Therefore, 5x =160 => x = 32
Total number of students = 8x + 5x = 13x
Total number of students = 13 * 32 = 416

Video solution: 7. Eesha bought two varieties of rice, costing 50 rs per kg and 60 rs pre kg each, and mixed them in some ratio. Then she sold the mixture at 70 rs per kg. Making a profit of 20 percent. What was the ratio of the mixture? 2:1

2:1

30.77%

2:4

2:4

25%

1:5

1:5

34.62%

1:8

1:8

9.62%

Selling price of the mixture = 70 and profit = 20%

Cost price of the mixture = 70×100/120=70×5/6
By applying alligation rule:

50(least price) 60(high price)
70 x (50/60) (new price *(least*high)
60-(175/3) : (175/3)-50

So ratio = 60−(175/3) : (175/3)-50

= 1 : 5 8. On a certain assembly line the rejection rate for hyundai i10’s production was 4 percent for hyundai i20’s production 8 percent and the two cars combined 7 percent . what was the ratio of hyundai i20’s production to hyundai i10’s production? 5:6

5:6

13.95%

2:1

2:1

44.19%

3:1

3:1

37.21%

4

4

4.65%

let the no of i10 cars be x and i20 be y
now the rejected i10 cars are 4x/100 and i20 cars are 8y/100

and it is given that 4x/100 +8y/100 = 7(x+y)/100
so we get y = 3x
so the ratio is 3:1 9. The savings of an employee equals income-expenditure. If the income of A, B, C is in the ratio 1:2:3, expenses  3:2:1. What is the order of employees A, B. C in the decreasing order of the size of their savings? a>c>b

a>c>b

13.73%

b>a>c

b>a>c

9.8%

b>c>a

b>c>a

9.8%

c>b>a

c>b>a

66.67%

income ratio should be=1:2:3
expense ratio should be=3:2:1
savings of a=1/6-(1/6*3/6)=1/12
savings of b=2/6-(2/6*2/6)=2/9
savings of c=3/6-(3/6*1/6)=5/12
so,savings ratio=1/12:2/9:5/12=3/36:8/36:15/36

Video solution: 10. The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of the teachers would then be 25 to 1 What is the present number of teachers? 61

61

10.64%

14

14

12.77%

15

15

59.57%

12

12

17.02%

Assume the present students and teachers are 30K, K
After new recruitments of students and teachers the strength becomes 30K + 50, K + 5 respectively. But given that this ratio = 25 : 1
⇒30K+50 / K+5=25 : 1⇒30K+50 / K+5=25 : 1
Solving we get K = 15
So present teachers are 15.

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