Ratio and Proportion - Coins Problems Shortcut Trick in Quantitative Aptitude

Determining number of coins from a given sum of money, kind of questions are asked in many competitive exams. So a fast shortcut method should be developed to solve these coins problems in quantitative aptitude or mathematics. So here is a shortcut method of solving these number of coins problems.

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?


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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
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
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
so number of 25 paise coins will  be =3x=40*3=120