Tips and Tricks on Ratio and Propertion

The problems on Ratio and Proportion can be easily solved by using some simple tips and tricks. Some of the Tips And Tricks and Shortcuts on Ratio And Proportion are mentioned below.

The problems on Ratio and Proportion can be easily solved by using some simple tips and tricks. Some of the Tips And Tricks and Shortcuts on Ratio And Proportion are mentioned below.

1. If x : y and z : a, then it can be solved as (x*z)/(y*a).


2. If x/y=z/a=b/c, then each of these ratios is equal to (x+z+e) ⁄(y+a+f)


3. If x/y=z/a, then y/x=a/z (Invertenao)


4. If x/y=z/a, then x/z=y/a (Alterenao)


5. If x/y=z/a, then (x+y)/y=(z+a)/a (Componendo)


6. If x/y=z/a, then (x-y)/y=(z-a)/a (Dividenao)


7. If x/y=z/a, then (x+y)/(x-y)=(z+a)/(z-a) (Componendo and Dividendo)


8. Four numbers x, y, z ana a are said to be in proportion if x : y = z : a. If on the other hand, x : y = y : z = z : a, then the four numbers are said to be in continued proportion.


9. Let us consider the ratios, x : y = y : z. Here y is called the mean proportional and is equal to the square root of the product of x and z i.e. y2 = x *z ⇒ y = √xz


10. If the three ratios, x : y, y : z, z : a is known, we can find x : a by the multiplying these three ratios x/a = x/y * y/z * z/a


11. If x, y, z, and a are four terms and the ratios x : y, y : z, z : a are known, then one can find the ratio x : y : z : a.

Question 1. Find the combined ratio of (1 : 6), (2 : 1), (3 : 2).

Options

A. 56/157

B. 1/2

C. 21/31

D. 1/5

Solution :

If we compound two or more ratio, then, a : b and c : d will become ac : bd. Therefore, $(1 : 6), (2 : 1), (3 : 2) = \frac{1}{6} * \frac{2}{1} * \frac{3}{2} = \frac{6}{12} = \frac{1}{2}$

Correct option: B

Question 1. Rupees 812.5 is divided among Suhas, Ragini, and Gautam in such a way that 3-times Suhas’s share, 2-times Ragini’s share and 4 times Gautam’s share is equal. Calculate their individual share.

Options

A. 246, 369, 184.5

B. 224, 350, 180.5

C. 375,250, 187.5

D. 285, 384, 195.5

Solution :

Let the Ragini, Suhas, and Gautam share be x, y, and z
Given, 2x = 3y = 4z.
Given, x + y + z = 812.5
Here, we will assign values of x and z in terms of y.
Therefore, y + 3y/2 + 3y/4 = 812.5
13y = 812.5*4
13y = 3250
y= 250
x = 375
z = 187.5
Therefore, individual shares are Suhas -375, Ragini – 250, Gautam – 187.5

Correct option: C

Question 1. A box has 210 coins of denominations one-rupee and fifty paise only. The ratio of their respective values is 13 : 11. The number of one-rupee coin is

Options

A. 65

B. 66

C. 75

D. 78

Solution :

Respective ratio of the NUMBER of coins;
= 13 : 11 × 2 = 13 : 22
Hence, Number of 1 rupee coins;
$\frac{{13 \times 210}}{{13 + 22}} = 78$

Correct option: D

Question 1. The ratio of water and milk in a 30 liter mixture is 7 : 3. Find the quantity of water to be added to the mixture in order to make this ratio 6 : 1.

Options

A. 30

B. 32

C. 33

D. 35

Solution :

Here,Let water = 7x and milk = 3x
Now,
7x + 3x = 30
x = 3
So, water = 7x = 7 × 3 = 21 liter
Milk = 3x = 3 × 3 = 9 liter

Now, we keep milk constant and add water to mixture to get ratio 6 : 1
Let water in this mixture = 6y and milk = y
We have, milk = 9 liter, so y = 9 liter
Water = 6y = 6 × 9 = 54 liter
Then extra water to be added is 33 liter

Correct option: C