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 problems in quantitative aptitude or mathematics. So here is a trick of solving these number of coins questions. You can learn the trick from below.
Learn Ratio and Proportion 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:
There are two solutions given for this question. first is normal method, second is shortcut method.
Normal method of solution of this type of problems is below:
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)
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)
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 trick for Ratio & Proportion Coins problem.
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.