Ratio & Proportion

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Directions: Each of the questions given below is followed by series of options among which you have to choose the best one. You can also review your choices by clicking into answer section.


1. A certain amount was divided between Santosh and Rajan in the ratio of 4 : 3. If Rahim’s share was Rs.2400, the total amount was.

A. Rs. 5600

B. Rs. 9600

C. Rs. 3200

D. Rs. 16800


Answer

                  Ans: Option A

       Explanation:

       Let S = 4x and R = 3x.

       Total amount = 7x.

       Then, 3x = 2400 so x= 800.

       Total amount = 7x = Rs.5600 


2. The number of seats available for Biology and Computer Science in a school is in the ratio 5:8. They are to be increased by 30% and 25% . Find the new ratio.

A. 6:10

B. 13:20

C. 3:4

D. 35:33


Answer

                  Ans: Option B

       Explanation:

       Let the number of seats be 5x and 8x.

       New ratio = (1.3*5x):(1.25*8x) = 6.5x:10x = 13:20 


3. Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

A. 2 : 5  

B. 3 : 5

C. 4 : 5  

D. 6 : 7


Answer

                  Ans: Option C

       Explanation:

       Let the third number be x.

       Then, first number = 120% of x =(120x/100)=6x/5

       Second number = 150% of x =(150x/100)=3x/2

       Ratio of first two numbers =(6x/5): (3x/2)= 12x : 15x = 4 : 5. 


4. According to a recipe, 400 grams of flour should be mixed with 500 grams of sugar to bake cookies. If I have only 300 grams of flour, how much sugar should I mix to maintain the same proportion?

A. 360

B. 380

C. 375

D. 400


Answer

                  Ans: Option C

       Explanation:

       Flour and sugar have to mixed in the ratio 4:5

       4:5:: 300:x

       4x=1500

        x=375

       375 grams of sugar should be mixed. 


5. The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?

A. 3 : 3 : 10         

B. 10 : 11 : 20

C. 23 : 33 : 60    

D. Cannot be determined


Answer

                  Ans: Option C

       Explanation:

       Let A = 2k, B = 3k and C = 5k.

      A's new salary = 115of 2k =(115/100)x 2k=(23k/10)

      B's new salary = 110of 3k =(110x 3k)/100)=33k/10

      C's new salary = 120of 5k =(120x 5k)/100= 6k

    New ratio (23k/10): (33k/10) : 6k= 23 : 33 : 60 


6. Three quantities X, Y and Z are such that XY=kZ where k is constant. Initially, X was at 4 and X:Y:Z was 2:3:4. If the value of Y is changed to 12 and Z is kept constant, find the value of X.

A. 2

B. 3

C. 5

D. 6


Answer

                  Ans: Option A

       Explanation:

       X:Y:Z=2:3:4

       X=4 Then, Y=6, Z=8

       XY=kZ

      4*6=k*8

      8k=24

      k=3,

      Then Y=12, Z=8

      X*12=3*8

      X=2 


7. If p : q = 3 : 4 and q : r= 8 : 9, then p : r is :

A. 1: 3

B. 2 : 3

C. 3 : 2

D. 1: 2


Answer

                  Ans: Option B

       Explanation:

       p/r = (p/q) * (q/r) = (3/4) * (8/9) = 2/3

       So,  p : q = 2:3 


8. 4 singers, 5 dancers and 3 comperes divide an amount of Rs.130000 among themselves such that 3 comperes get as much as 2 dancers and 3 dancers get as much as 2 singers. Find the amount received by a singer.

A. Rs.18000

B. Rs.13000

C. Rs.15000

D. Rs.10000


Answer

                  Ans: Option C

       Explanation:

       4S+5D+3C=130000

       3C=2D

       3D=2S

       S=3D/2

       [4*(3D/2)]+5D+2D = 130000

       6D+5D+2D = 130000

       13D = 130000

       D = Rs.10000

       S=3D/2 = Rs.15000 


9. In a mixture 60 liters, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quantity of water to be further added is:

A. 20 liters           

B. 30 liters

C. 40 liters           

D. 60 liters


Answer

                  Ans: Option D

       Explanation:

       Quantity of milk = (60/3) x2 liters = 40 liters.

       Quantity of water in it = (60- 40) liters = 20 liters.

       New ratio = 1:2

       Let quantity of water to be added further be x liters.

       Then, milk : water =40/(20 + x)                   .

    Now, 40/(20 + x)= 1/2

       20 + x= 80

       20 + x = 80

       x = 60.

       Quantity of water to be added = 60 liters. 


10. If a+b : b+c : c+a = 6 : 7 : 8 and a + b + c = 14, then the value of c is : . [C.B.I. 1993]

A. 6

B. 8

C. 7

D. 14


Answer

                  Ans: Option D

       Explanation:

       (a/3) = (b/4) = (c/7) then a = 3k, b = 4k, c = 7k

       a+b+c/c = 3k+4k+7k/7k = 14k/7k = 2 


11. Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:

A. 27      

B. 33

C. 49      

D. 55


Answer

                  Ans: Option B

       Explanation:

       Let the numbers be 3x and 5x.

       Then,     (3x – 9)/(5x – 9)   =(12/23)

       or, 23(3x – 9) = 12(5x – 9)

        or, 9x = 99

        Therefore, x = 11.

        The smaller number = (3 x 11) = 33.


12. Rs. 120 are divided among A, B, C such that A’s share is Rs. 20 more than B’s and Rs. 20 less than C’s. What is B’s share?

A. Rs. 10

B. Rs. 20

C. Rs. 15

D. Rs. 25


Answer

                  Ans: Option B

       Explanation:

       Let C = x. Then A = (x—20) and B = (x—40).

       or, x + x – 20 + x – 40 = 120

       or, x=60.

    A:B:C = 40:20:60 = 2:1 :3.

    B’s share = Rs.120*(1/6) = Rs. 20. 


13. Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

A. 2 : 3 : 4            

B. 6 : 7 : 8

C. 6 : 8 : 9           

D. None of these


Answer

                  Ans: Option A

       Explanation:

Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.

Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).

 (140/100)* 5x , (150/100)* 7x  and (175/100)* 8x         

 7x , (21x/2) and 14x

 The required ratio = 7x : (21x/2) : 14x

                               = 14x : 21x : 28x

                               = 2 : 3 : 4. 


14. An alloy is to contain copper and zinc in the ratio 9 :4. The zinc required (in kg) to be melted with 24 kg of copper, is 7

A. 10 and 2/3

B. 9 and 2/3

C. 10 and 1/3

D. 9


Answer

                  Ans: Option C

       Explanation:

       9:4: 24 : x

       ⇒ 9x = 4 * 24

       ⇒ x = (4*24)/9  = 32/3 Kg. hence 10 and 1/3 


15. A class has 90 students. If the ratio of boys and girls is 7:8, find the number of boys in the class.

A. 48

B. 42

C. 60

D. 70


Answer

                  Ans: Option B

       Explanation:

       7x+8x=90

       or, 15x=90

       So, x=6

       Number of boys=7x=42 


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