Ratio and Proportion Questions and Answers

Exercise


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Q 1

A bag contains 50 p, 25 p and 10 p coins in the ratio 5:9:4, amounting to Rs.206. Find the total number of coins in the bag.


A)  

40

B)  

180

C)  

360

D)  

720


Correct Option - D

Explanation

Let the number of 50p, 25p and 10p coins be 5x, 9x and 4x.

(5x*50)+(9x*25)+(4x*10) = 20600

250x+225x+40x=20600

515x=20600

x=40

Total number of coins

= 18x

= 720

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Q 2

The cost of a precious stone varies as the square of its weight. A diamond weighing 10 decigrams costs Rs. 2600. The loss incurred when it breaks into two pieces whose 


A)  

Rs.168

B)  

Rs.872

C)  

Rs.1352

D)  

Rs.1248


Correct Option - D

Explanation

The cost varies as the square of the weight.

Weight of the diamond = 10 dg

Weight of the two pieces = 6dg, 4dg

Value of the two pieces

= 2600*(36+16)/100

= 2600*52/100

Loss in value

= 2600*48/100

= Rs.1248

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Q 3

An sum of 150$ is divided among A,B and C such that for each dollar A gets, B gets 60 cents and C gets 40 cents. Find B's share.


A)  

45$

B)  

60$

C)  

30$

D)  

40$


Correct Option - A

Explanation

If A gets 100 cents,

B gets 60 cents

C gets 40 cents

A:B:C=100:60:40=5:3:2

B's share

= (3/10)*150

= 45$

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Q 4

X, Y and Z are quantities of the same kind such that X:Y=5:8 and Y:Z=4:7. Find X:Z.


A)  

32:35

B)  

67:56

C)  

5:14

D)  

5:7


Correct Option - C

Explanation

X:Z=(X:Y)*(Y:Z)

   =(5:8)*(4:7)

  = (5/8)*(4/7)

    = 5/14

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Q 5

A box containing a dozen apples is opened and a few of the apples are found to be rotten. Which of the following may be the ratio of fresh apples to rotten apples?


A)  

4:7

B)  

3:1

C)  

5:3

D)  

3:2


Correct Option - B

Explanation

Let X and Y be the number of fresh apples and rotten apples.

X+Y=12

Ratio = X:Y

If the ratio simplifies to a:b,

a+b has to be a factor of 12.

3+1=4 is a factor of 12. Hence (B) can be the ratio.

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Q 6

The sum of cubes of two numbers is 280. If the numbers are in the ratio 2:3, find the smallest number.


A)  

4

B)  

6

C)  

3

D)  

2


Correct Option - A

Explanation

Let the numbers be 2x and 3x.

(2x)³+(3x)³=280

8x³+27x³=280

35x³=280

x³=8

x=2

The numbers are 4 and 6.

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Q 7

The sum of squares of three numbers is 280. If the numbers are in the ratio 3:5:6, find the greatest number.


A)  

8

B)  

6

C)  

12

D)  

18


Correct Option - C

Explanation

Let the numbers be 3x,5x and 6x.

(3x)²+(5x)²+(6x)²=280

9x²+25x²+36x²=280

70x²=280

x²=4

x=2

The greatest number is 6x=12.

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