Question

sudha has ₹45 in the form of ₹1 and 50 paise coins.if she has 70 coins all,find the number of coins of each denomination.

Answer 1

Solutions :-

We have,

Sudha has ₹ 45 in the form of ₹ 1 and 50 paise (₹ 0.5) coins.
Total coins = 70

Let the ₹ 1 be x
and ₹ 0.5 be y

x + 0.5y = 45 _____ (i)
x + y = 70 ______(ii)

Here, let us eliminate the x term.

Subtract equations (ii) from (i),

(x + y) - (x + 0.5y) = 70 - 45
=> 0.5y = 25
=> y = 25/0.5 = 50

Substitute the value of x in equation (i) or equation (ii) to find the value of x. Substituting the value of y in the first equation, we have,

x + 50(0.5) = 45
=> x + 25 = 45
=> x = 45 - 25 = 20

Answer :
Numbers of ₹ 1 coins = 20
Numbers of 50 paise coins = 50

Answer 2

Solutions :-

Given :

Sudha has ₹ 45 in the form of certain number of ₹ 1 (100 paise) and 50 paise coins.
Total number of coins = 70

Let the ₹ 1 and 50 paise coins be x and y respectively.

100x + 50y = 4500 ______(1) (taking the money in paise)
x + y = 70 ______ (2)

We have to eliminate the x term, therefore equate the coefficient of x in both the equations.

(100x + 50y = 4500)1 => 100x + 50y = 4500 ___(3)
(x + y = 70)100 => 100x + 100y = 7000 ____(4)

Subtract equation (3) from (4),

(100x + 100y) - (100x + 50y) = 7000 - 4500
=> 100x + 100y - 100x - 50y = 2500
=> 100x - 100x + 100y - 50y = 2500
=> 50y = 2500
=> y = 2500/50 = 50

Now,
Substitute the value of y in equation (1) or equation (2)

=> x + y = 70
=> x + 50 = 70
=> x = 70 - 50 = 20

Hence,
Numbers of ₹ 1 coins = x = 20
Number of 50 paise coins = y = 50