# 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?

solution:

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

all ratio and proportion formulas and shortcuts are listed here

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

All Shortcut Formulas of Ratio and Proportion are discussed here

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)

Boat and Stream Questions shortcuts are listed here

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)

shortcut formulas for Profit and Loss Problems-Learn how to solve them Quickly

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