Question

Sumitra has Rs34 in 50 paise and 25 paise coins.If the number of 25 paise coins is twice the number of 50 paise coins,how many coins of each kind does she have?​

Answer 1

Given :-

• Sumitra has total Rs 34

• In form of 50 paise and 25 paise .

• 25 paise is twice of 50 paise .

To Find :-

Number of the coins of 50 and 25 paise .

Solution :-

Let's assume that number of 50 paise coins is x .

As 25 paise coins is twice of 50 paise coins .

So the number of 25 paise coins is 2x .

The sum of these coins is Rs 34.

Converting Rs 34 into paise .

→ 34 = 3400 paise

→ 50x + 25(2x) = 3400

→ 50x + 50x = 3400

→ 100x = 3400

→ x = 3400/100

→ x = 34 .

So, number of 50 paise coins is 34.

→ Number of 25 paise coins = 2x

→ 2(34) = 68 coins.

Number of 25 paise coins is 68 .

Verification -

→. 50(34) + 25(68) = 1700+1700

→ 3400 paise = Rupees 34 .

Hence verified .

Answer 2

Sumitra has total amount of ₹ 34 with her.

The denomination making the amount of ₹ 34 are 50 paise and 25 paise.

The number of 25 paise coins is twice the number of 50 paise coins.

So, let's make some assumption before finding the number of 50 paise and 25 paise coin Sumitra has.

Let Sumitra have x number of 50 paise coins.

And,let her have y number of 25 paise coins.

The summation of these x and y number of coin is ₹ 34.

It is known that, ₹ 1 = 100 paise.

The amount with Sumitra is ₹ 34.

Convert the unit ₹ to paise.

•°• ₹ 34 = 34 × 100 = 3400 paise.

Here we can have our first equation.

=> $\sf{50x+25y=3400}$

=> $\sf{50x=3400-25y\:\:\:\:\:(1)}$

Also,she has 25 paise coin as much as twice the number of 50 paise coin.

Here we will have the second equation.

=> $\sf{y = 2x}$

=> $\sf{\dfrac{y}{2}=x\:\:\:\:\:(2)}$

Use the value of x from 2nd equation in first equation and move ahead.

=> $\sf{50x=3400-25y}$

=> $\sf{50\Big(\dfrac{y}{2}\Big)=3400-25y}$

=> $\sf{\dfrac{50y}{2}=3400-25y}$

=> $\sf{50y=2(3400-25y)}$

=> $\sf{50y=6800-50y}$

=> $\sf{5y=6800-5y}$

$\sf{=>\:5y+5y=680...\rm{\big[Dividing\: throughout\:by\:10\big]}}$

=> $\sf{10y=680}$

=> $\sf{y=\dfrac{680}{10}}$

=> $\sf{y=68}$

Now, just use this value of y in any of the above two equation to find the number of x coins.

Substitute y 's value in equation (2),

=> $\sf{\dfrac{y}{2}=x}$

=> $\sf{\dfrac{68}{2}=x}$

=> $\sf{34=x}$

$\tt{\underline{\red{Number\:of\:50\:paise\:coin\:=\:68}}}$

$\tt{\underline{\red{Number\:of\:25\:paise\:coin\:=\:34}}}$