Ratio and Proportion Questions and Answers Quiz 1

By Shiva
May 04, 2017
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1 . A bag contains 50 p, 25 p and 10 p coins in the ratio 5 : 9 : 4, amounting to Rs.206. Find the number of coins of each type respectively.

A.    200, 305, 106
B.    210, 350, 148
C.    200, 360, 160
D.    200, 160, 180
2 . The ratio of length to width of a rectangular sheet of paper is 5 : 3. If the width of the sheet is 18 cm, find its length?

A.    10 cm
B.    20 cm
C.    25 cm
D.    30 cm
3 . The ratio between the number of men and women in an office is 5 : 7. If the number of women working in the office is 56. Find the number of men working in the office?

A.    40
B.    50
C.    45
D.    60
4 . If (a + b) : (a - b) = 15 : 1, then the value of $a^ 2$ - $b^ 2$ is :

A.    56
B.    15
C.    112
D.    8
5 . The students in three classes are in the ratio of 2 : 3 : 4. If 40 students are added in each class, the ratio becomes 4 : 5 : 6. Find the total number of students in all the three classes is :

A.    270
B.    180
C.    126
D.    135
6 . Two equal containers are filled with the mixture of milk and water. The concentration of milk in each of the container is 20% and 25% respectively. What is the ratio of water in both the containers respectively?

A.    15:16
B.    16:15
C.    4:5
D.    5:4
7 . A camel pursue an elephant and takes 5 leaps for every 7 leaps of the elephant, but 5 leaps of elephant are equal to 3 leaps of camel. What is the ratio of speeds of camel and elephant?

A.    21:25
B.    24:23
C.    25:21
D.    23:24
8 . The age of Sachin is 4 times that of his son. Five years ago Sachin was nine times as old as his son was at that time. The present age of the Sachin is :

A.    25 years
B.    36 years
C.    32 years
D.    48 years
9 . Bhanu and Shafeeq started a business by investing Rs.36,000 and Rs.63,000. Find the share of each respectively, out of an annual profit of Rs.5500.

A.    2000,5500
B.    2500,4500
C.    3000,4000
D.    2000,3500
10 . If A : B = 3 : 4 and B : C = 8 : 9, then A : C is :

A.    1:3
B.    3:2
C.    2:3
D.    1:2
Answers & Solutions
1 .    
Answer : Option C
Explanation :
Let the number of 50 p, 25 p and 10 p coins be 5x, 9x and 4x respectively.
Then, $5x\over2$+$9x\over4$+$4x\over10$ = 206
$50x+45x+8x=4120$
$103x=4120$
$x=40$
Number of 50 p coins = (5 × 40) = 200; number of 25 p coins = (9 × 40) = 360;
number of 10 p coins = (4 × 40) = 160
2 .    
Answer : Option D
Explanation :
Let the length of sheet of paper be x cm. Then the ratio of length to width = x : 18
Thus,
x : 18 = 5 : 3
x × 3 = 18 × 5
x = 30
Hence the length of paper = 30 cm
3 .    
Answer : Option A
Explanation :
5 : 7 = x : 56 (suppose number of men = x)
x = 40 (by the first property)
Therefore, number of men in the office = 40
4 .    
Answer : Option B
Explanation :
$(a+b)\over(a-b)$=$15\over1$
$a\over b$ = $8\over7$ (by compnendo and dividend)
Therefore, $a^ 2$ - $b^ 2$ = 64-49 = 15
5 .    
Answer : Option B
Explanation :
2x + 40 = 4y … (i)
3x + 40 = 5y …. (ii)
4x + 40 = 6y ….. (iii)
Therefore 2x = 40
x = 20
Hence, total number of students = 2x + 3x + 4x = 9x = 9 × 20 = 180
6 .    
Answer : Option B
Explanation :
Milk $\,\,\,\,\,$ 20% $\,\,\,\,\,$ 25%
Water $\,\,\,$ 80% $\,\,\,\,$ 75%
Therefore, required ratio =$80\over75$=$16\over15$ or 16:15
7 .    
Answer : Option C
Explanation :
Ratio of speed of camel and elephant = $5\over3$:$7\over5$=$5\over3$$\times$15:$7\over5$$\times$15=25:21
8 .    
Answer : Option C
Explanation :
Let the age of son is x years, then the age of Sachin will be 4x years.
So, (4x - 5) = 9 (x - 5) | x = 8
So, age of Sachin is 32 years.
9 .    
Answer : Option D
Explanation :
Ratio of shares of Bhanu and Shafeeq = 36000 : 63000 = 4 : 7
So, Share of Bhanu = 5500 × $4\over11$ = Rs.2000
And share of Shafeeq = 5500 x $7\over11$ = Rs.3500
10 .    
Answer : Option C
Explanation :
[$A\over B$ = $3\over 4$, $B\over C$=$8\over 9$]
$A\over C$= [$A\over B$$\times$$B\over C$] = [$3\over 4$$\times$$8\over 9$] = $2\over 3$
A:C = 2:3
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