Question

Revathy collected a sum of Rs.150 in a piggy bank. She had put only 2, 5
and 10 coins into it. If 10 and 5 coins are in the ratio 3:7 and there are a total
of 30 coins, find the number of coins of each type.

Answer 1

SOLUTION

GIVEN

• Revathy collected a sum of Rs. 150 in a piggy bank.

• She had put only 2, 5 and 10 coins into it.

• If 10 and 5 coins are in the ratio 3:7

• There are a total of 30 coins

TO DETERMINE

The number of coins of each type.

EVALUATION

Here it is given that, Revathy collected a sum of Rs. 150 in a piggy bank. She had put only 2, 5 and 10 coins into it. If 10 and 5 coins are in the ratio 3:7

Suppose number of 10 coins = 3x and 5 coins = 7x

Now there are a total of 30 coins

So number of 2 coins

= 30 - 3x - 7x

= 30 - 10x

So the value of all coins

= 2(30- 10x) + (5 × 7x) + ( 10×3x)

= 60 - 20x + 35x + 30x

= 45x + 60

So by the given condition

$\sf{45x + 60 = 150}$

$\sf{ \implies \: 45x = 150 - 60}$

$\sf{ \implies \: 45x = 90}$

$\sf{ \implies \: x = 2}$

Hence

The number of 2 coins = ( 30 - 20 ) = 10

The number of 5 coins = 14

The number of 10 coins = 6

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