## Aug 11, 2015

### APTITUDE SHORTCUT & MIND TRICK FOR SOLVING RATIO AND PROPORTION PROBLEMS

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Maths Shortcut and Mind Trick for Solving Ratio and Proportion Problems
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Q) If in a bag Rupee 1, 50 p and 10 p coins are present in the ratio as 5:8:10 amounting to Rs.400. Then find the total number of 10paise coins present in the bag?

We are given Following Information:

Denomination of coins Present in the bag = 50p, 10p, 1 Rupee
Total Amount = Rs 400
Ratio of coins = 5 : 8 : 10

Solution:

First we solve this question by Normal Method:

As we Know, 1 Rupee= 100 Paise

Therefore, Let the total number of 1Rupee (100 p), 50p, 10p coins present are 5x, 8x and 10x respectively.

As the total amount we are given in the above question in Rupees i.e Rs 400.

Therefore First we have to convert the denomination of 50p and 10p into Rupee denomination.

As, 100 P = 1Rupee
1 P = 1/100 Rupee
50 P = (1/100)* 50 Rupee= ½ Rupee

Similarly, 10 P = [(1/100)* 10] Rupee = [1/10] Rupee

Also, 1 Rupee= 1 Rupee

Now, Multiply the converted rupees value with the respected given ratios,

Therefore, We get
=1×5x + (½ ×8x) + [(1/10)×10x]
=5x+(4x)+(x)
=10x

According to Given Question,
10x = 400
x = [400/10] = 40

Now, We have to find the total number of 10p coins present in the bag.

Therefore, No. of 10p coins present in the bag = 10x = [10×40] = 400 coins

Therefore, 400 Coins is the required answer.

Now we will solve this question direct by Shortcut method:

As we have: 5×100p: 8×50p: 10×10p

Therefore, Sum of all Parts= 10
And 10= Rs.400
So, One part of x = ?
x = Rs. 400 /10 = 40

There for total no. of 10p coins = 10×40
= 400 coins.

Thank You Friends!! J