Ratio and Proportion Practice Problems with Solutions

Friends, in our last post we have discussed about the basic concepts and some shortcut techniques of Ratio and Proportion Problems. In this post we shall discuss some model practice problems.

1. Rs. 630 is to be distributed amongst Ramu and Kiran in the proportion 7:11. How much would Kiran get ?

Solution :

Total amount = 630

So, total parts = 7+11 = 18

Second part (Kiran's share) = 630 x (11/18) = Rs. 385    

So the answer is Rs. 385

if they asks for Ramu's share then

 Ramu's share = 630 x (7/18) = Rs. 245

2. The ratio of two numbers is 3 : 4. The L.C. M of the numbers is 180. What are those numbers?

Solution :

Say required numbers are 3k, 4k

the L.C.M of 3k, 4k is = 12k

So, 12k = 180 => K = 15

So, required numbers 3k = 3 x 15 = 45

4k = 4 x 15 = 60

3. The ratio of two numbers is 5:7. If you subtract "3" from those numbers, the ratio is 2:3. What are those numbers?

Solution :

Say, the required numbers are 5k, 7k

then (5k-3) / (7k-3) = 2 / 3      [according to the given data]

=>  15k-9 = 14k - 6

=>  k = 3

So, required numbers are 15 and 21.

Shortcut Technique :

1st ratio = 5 : 7            2nd ratio = 2:3

1st number = (3 x 5) / (15 - 14)  = 15

2nd number = (3 x 7) / (15 - 14) = 21

4. The ratio of two numbers is 4 : 5. The difference between those squares is 81. What are those numbers ?

Solution :

Say the required numbers are 4k, 5k

        then  (5k) ²-(4k) ² = 81 

            9k² = 81

          = >  k² = 9  => k = 3

          So, required numbers 4 x 3 = 12           and          5 x 3 = 15

5. In a committee of 48 members, the ratio of Men and Women are 3 : 1. How many women should join the committee to make the ratio 9 : 5 ?
Solution :

The total members of the committee = 48

The ratio of Men and Women are = 3 + 1 = 4

Total number of men = 48 x (3/4) = 36

Total number of women = 48 x (1/4) = 12

say the required women are k.

So, total women  will be 12+k

so, 36 / (12+k) = 9 / 5

then 9 (12 + k) = 36 x 5

 = >  108 + 9k = 180  => k = 8

So, the number of required women is 8

Shortcut Technique :

The number of Required women =  48 / ((9-5) + 3-1))  = 8


6. A: B = 2 : 3, B : C = 4 : 5  and C : D = 5 : 7. then A : B : C :  D is ?
Solution :

To equate the ratios, the B terms and  C terms should be same. But here the value of Bs in the first ratio and second ratio are not equal. In the same way, the values of Cs in the second and third ratios are not equal. SO you should equate them first.

A : B = 2 : 3
you can write this ratio as 8 : 12 (just multiplied both sides with 4)

B : C =  4 : 5
you can write this as 12 : 15 (multiplied both sides with 3)

C : D = 5 : 7
you can write this as 15 : 21 (multiplied both sides with 3)

So,

A : B : C : D = 8 : 12 : 15 : 21


Shortcut Method :
A : B : C : D =

(2 x 4 x 5 ) : ( 3 x 4 x 5 ) : (3 x 5 x 5) : (3 x 5 x 7)

= 40 : 60 : 75 : 105

by simplifying them you will get,

8 : 12 : 15 : 21


7. The ratio of milk and water in a mixture of 50 liters is 3 : 2. How many liters of water should we add to make this ratio 2 : 3 ?
Solution :

Milk in the 50 liters mixture = (3 / (3+2)) x 50  = 30 Liters

Water = 50 - 30 = 20 Liters

assume that you should mix K liters of water to make the ratio 2 : 3

that means  (30 / (20 + k)) = 2 / 3

2k + 40 = 90

=> k= 25 Liters


Shortcut Method :

Required quantity of water 

=  ( 50 * (3² – 2² ) / (2 * (3+2))  = 25 Liters

8. If we subtract a number from 8 : 13, it became 3 : 5. What is that number ?
Solution :

Say the number is K,

so,    (8-k) / (13-k)  = 3/5

=>  3 (13-k) = 5 (8-k)

=> 39 - 3k = 40-5k

=> 5k - 3k = 40-39

=> k = 1/2


9. The total of two numbers is 49. And the ratio between those two numbers is 2:5. What are those numbers?
Solution :
Assume that those two numbers are 2, 5        (as they are in the ratio of 2:5)
So, the total of those numbers is = 2+5 = 7

But, given that the total is 49

so,  the first number is = (2/7)*49 = 14

as you got the first number, the 2nd number is
(14*5) / 2  = 35          [or you can try (5/7)*49]


10.  In an army there are 2100 Soldiers. They have food reserves for 50 days. Some people among them left on leave. Now they can utilize their food reserves for 75 days. How many soldiers left on leave?
Solution :

Assume that the soldiers who left on leave are K

So,

Soldiers                    Days
2100                          50
2100 - k                     75

if the number of soldiers reduces, the number of days increases. Then,

75 : 50 :: 2100 : (2100 - k)

(75/50) = ((2100/ (2100-k))

4200 = 6300 - 3k

=>3k = 2100  => k = 2100/3  = 700


Shortcut Method :
Soldiers left on leave are = (A ( B- C)) / B

here, A = 2100
B = 75  and C = 50

=>  (2100 (75-50)) / 75

= (2100 x 25) / 75  = 700


That's all for now friends. If you have any doubts on the methods explained in this post, then feel free to clarify your doubts by using the comments section below. In our next post we shall discuss more model practice problems on Ratio and Proportion which are of higher difficulty level. All the Best and Happy Reading :)

10:08 - By Unknown 0