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Algebraic MCQ 1(types of coins and total amount)

Algebraic MCQ 1: A bag contains equal number of Rs.5, Rs.2 and Re.1 coins. If the total amount in the bag is Rs.1152, find the number of coins of each kind?
a) 432                  b) 288                 c) 144             d) 72

Solution:

We know that if there are suppose five 10 Rs coins, then amount made by these will be = ​\( 10\times5=Rs 50 \)

Similarly,

If we suppose that there are ‘x’ coins of each type

i-e 5 Rs coins =x, ———– then, total amount made by 5Rs coins = 5x

2 Rs coins =x ———— then, total amount made by 2 Rs coins = 2x

1 Rs coins =x ———— then, total amount made by 1 Rs coins = 1x

i-e total amount ​\( = 5x+2x+x \)

But it is given that total amount made by given number of coins is 1152

So,

\[ 5x+2x+x=1152 \]

\[ 8x=1152 \]

\[ x=144 \]

i-e 5 Rs coins are 144 in number

2 Rs coins are 144 in number

1 Rs coins are 144 in number

 

For a check, you multiply  5 with 144, 2 by 144 and 1 by 144 and then take a sum — it will be 1152

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