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Only Rs 1 and Rs 2 coins are in Aruna's possession. If she has 50 total coins and has Rs 75 in her possession, then there are 50 Rs 1 coins and 75 Rs 2 coins, respectively.

Then the number of Rs 1 and Rs 2 coins are

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50 and 35

35 and 20

25 and 25

60 and 45

answer is C.

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Detailed Solution

It is given that Aruna has total 50 coins of Rs 1 and Rs 2.
Let the Rs 1 coin's number be

p

and the Rs 2 coin's number be

q

.
Then,

p + q = 50

\Rightarrow q = 50 - p

… (1)
Get the equation expressed in terms of the whole sum of money.
Since entire sum is Rs 75, it can be expressed as,

1 \times p + 2 \times q = 75

\Rightarrow p + 2 q = 75

… (2)
Substitute the value of

q

from equation (1) in equation (2),

⇒ p + 2 q = 75 ⇒ p + 2 50 − p = 75 ⇒ p + 100 − 2 p = 75 ⇒ 100 − p = 75

⇒ − p = 75 − 100 ⇒ − p = − 25 ∴ p = 25

Substitute

p = 25

in equation (2) we get,

⇒ p + 2 q = 75 ⇒ 25 + 2 q = 75 ⇒ 2 q = 75 − 25

⇒ 2 q = 50 ⇒ q = 502 ∴ q = 25

So, the numbers of Rs1 and Rs2 coins are 25 and 25 respectively.
Therefore, option 3 is correct.

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