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.

  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

Revise and learn Formulas for Ratio and Proportions instantly.

Tips and Tricks and Shortcuts

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