Tips And Tricks and Shortcuts on Ratio And Proportion

Ratio and Proportion Tips and Tricks and Shortcuts

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.

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

Question 1.

Find the combined ratio of (5 : 6), (7 : 9), (10 : 11).

A. 56/157
B. 65/99
C. 21/31
D. 1/5

Correct answer  – 65/99

Solution:

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
= 65/99

Type 2: Tricks and Shortcuts

Distributing Any Quantity Based On Ratios

Question 2.

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

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

Type 3: Ratio and Proportions Tips and Tricks

Coins Based Ratio Problems

Question3.

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.

A. 2800
B. 2000
C. 3500
D. 3000

Correct answer – 3000

Solution:

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

Question 4.

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.

A. 9
B. 15
C. 12
D. 10

Correct answer – 9

Solution:

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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