Tips And Tricks and Shortcuts on Ratio And Proportion
Ratio and Proportion Tips and Tricks and Shortcuts
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.
- If x : y and z : a, then it can be solved as (x*z)/(y*a).
- If x/y=z/a=b/c, then each of these ratios is equal to (x+z+e) ⁄(y+a+f)
- If x/y=z/a, then y/x=a/z (Invertenao)
- If x/y=z/a, then x/z=y/a (Alterenao)
- If x/y=z/a, then (x+y)/y=(z+a)/a (Componendo)
- If x/y=z/a, then (x-y)/y=(z-a)/a (Dividenao)
- If x/y=z/a, then (x+y)/(x-y)=(z+a)/(z-a) (Componendo and Dividendo)
- 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.
- 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
- 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
- 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.
Note – There are four types of Ratio and Proportion problems that are as follows :-
Type 1: Ratio and Proportions Tricks
Compound Ratio Based On Individual Ratios
Find the combined ratio of (5 : 6), (7 : 9), (10 : 11).
Correct answer – 65/99
If we compound two or more ratio, then, a : b and c : d will become ac : bd. Therefore, (5 : 6), (7 : 9), (10 : 11) = 5/6 * 7/9 * 10/11 = 350/594
Type 2: Tricks and Shortcuts
Distributing Any Quantity Based On Ratios
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.
A. 246, 369, 184.5
B. 224, 350, 180.5
C. 375,250, 187.5
D. 285, 384, 195.5
Correct answer – 375, 250, 187.5
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
x = 375
z = 187.5
Therefore, individual shares are Suhas -375, Ragini – 250, Gautam – 187.5
Type 3: Ratio and Proportions Tips and Tricks
Coins Based Ratio Problems
Geeta has 1800 rupees in the denomination of 5 paisa, 25 paisa, and 75 paisa in ratio 6 : 3 : 1. Calculate how many 25 paisa coins he has.
Correct answer – 3000
Let the number of 5 paisa coins be 6x
Let the number of 25 paisa coins be 3x
Let the number of 75 paisa coins be x
Then, 5*6x/100 + 25*3x/100 + 75x/100 = 1800
=> 180x/100 = 1800
Therefore, x = 1800*100/180
x = 1000
Hence, 25 paisa coins = 3*1000 = 3000
Type 4: Tips and Tricks
Mixtures & Addition Based Ratio Problems
A mixture of sugar and water is in the ratio 3 : 2. A man adds 9 liters of water, and the mixture comes in the ratio of 3 : 5. Find the quantity of sugar in the new mixture.
Correct answer – 9
Let water be 2x, and sugar is 3x.
Given, 3x/2x+9 = 3/5
5x = 2x + 9
3x = 9
x = 3
Therefore, quantity of sugar = 3 * 3 = 9 liters
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