## Ratio and Coins Problem Shortcut Tricks

Below is a question for example:A bag contains rs. 90 in coins on 50 paise, 25 paise and 10 paise. if the coins are in the ratio 2:3:5 , then determine the number of 25 paise coins?

solution:

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**There are two solutions given for this question. first is normal method, second is shortcut method.**

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Normal method of solution of this type of problems is below:

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since the ratio is 2:3:5

so

let number of 50 paise coins is=2x (as the given ratio for 50 paise coins is 2)

number of 25 paise coins is= 3x (as the given ratio for 25 paise coins is 3)

and number of 10 paise coins is= 5x (as the given ratio for 10 paise coins is 5)

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so the value of 50 paise coins = 2x/2 =x (since there are two 50 paise coins in 1 rupee)

and value of 25 paise coins = 3x/4 (since there are four 25 paise coins in 1 rupee)

and value of 10 paise coins = 5x/10=x/2 (since there are ten 10 paise coins in 1 rupee)

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adding all the money and equating

x+(3x/4)+(x/2) = 90

4x+3x+2x=360

9x=360

x=40

so number of 25 paise coins will be

3x= 40*3=120

**Below is the simple SHORTCUT for the above problem i.e. coins problems**

in this type of questions, first multiply the ratios by x and then divide them respectively so as you have to convert them in rupees and add them all so that you can get the value of x by equating it to the money given.

(2x/2)+(3x/4)+(5x/10) = 90

(2x is divided by 2 because 2x is for 50 paise coins and there are 2 fifty paise coins in 1 rupee and similarly 3x is divided by 4 because there are four 25 paise coins in 1 rupee and similarly 5x is divided by 10 because there are 10 ten paise coins in 1 rupee)

4x+3x+2x= 360