In my elder brother's bag there are 350 with the coins of ₹1 and ₹50 paise together.My sister has put out 1/3 part of 50 paise coins from the bag and in that place equal number of coins of ₹1 she has put into the bag and now the total amount of money in the bag is 400 . Let us calculate and write the original number of coins of ₹1 and ₹50 paise kept at first separately in my brother's bag.
Answers
Given :-
- Total amount in beg = Rs.350 with the coins of ₹1 and ₹50 paise together.
- Sister took out = (1/3) of 50 paise coins and put equal number od Rs.1 coins .
- Now total amount in beg = Rs.400 .
To Find :-
- original number of coins of ₹1 and ₹50 paise .
Solution :-
Let us assume that, Original number of Rs.1 coins were x and 50 paise coins were y .
so,
→ 1 * x + (1/2) * y = 350
→ 2x + y = 700 -------------- Eqn.(1)
now,
→ coins sister took out = (1/3) of y = (y/3)
and,
→ coins she added of Rs.1 = (y/3)
then,
- Total coins of Rs.1 = x + (y/3) = (3x + y)/3
- Total coins of 50 paise = y - y/3 = (2y/3)
so,
→ Total amount in beg = Rs.400
→ 1 * (3x + y)/3 + (1/2) * (2y/3) = 400
→ (3x + y)/3 + (y/3) = 400
→ 3x + y + y = 1200
→ 3x + 2y = 1200 -------------- Eqn.(2)
Multiply Eqn.(1) by 2 and subtracting Eqn.(2) from result,
→ 2(2x + y) - (3x + 2y) = 2*700 - 1200
→ 4x - 3x + 2y - 2y = 1400 - 1200
→ x = 200 (Ans.)
putting value of x in Eqn.(1), we get,
→ 2 * 200 + y = 700
→ 400 + y = 700
→ y = 700 - 400
→ y = 300 (Ans.)
Hence, original number of coins of ₹1 and ₹50 paise kept at first separately in my brother's bag were 200 and 300 respectively .
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