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Aptitude Shortcuts and Mind Tricks for Ratio and Proportion

QUESTION:

A bag contains 1rupee, 50 paise and 10 paise coins in the ratio 3:4:10 amounting to

Rs.102. Find the number of 10paise coins?

GIVEN:

Denomination of coins = 50p, 10p, 1 rupee

Total amount = Rs.102

Ratio of coins = 3:4:10

SOLUTION:

NORMAL METHOD

Let the number of 1rupee (100 paise), 50p, 10p coins be 3x, 4x and 10x respectively

Since the total amount is given in Rupees (102), the 50p and 10p has to be converted

into rupees

Therefore,

1 rupee = 1 rupee

50p = [50/100] = rupee

10p = [10/100] = [1/10] rupee

Multiply the converted rupees with the given ratios so,

13x + ( 4x) + [(1/10)10x]

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3x+(4x/2)+(10x/10)

We will get,

3x + 2x + 1x = 102

=> 6x = 102

=> x = [102/6] = 17

Now, the number of 10p coins are asked in the question, the ratio term of 10p =10x

Therefore, no. of 10p coins in the bag = 10x = [1017] = 170 coins

SHORT METHOD

3100p: 450p: 1010p

3100p: 450p: 1010p

300: 200: 100

3 : 2 : 1

(Add the above three ratios) 6

Sum of all parts 6= Rs.102

Single part 1=?

x = Rs. 102 /6 = 17

There for no of 10p = 10

17 = 170coins