Question

a bag contains 25p coins, 50p coins and 1 rupee coins whose

values are in the ratio of 8:4:2. The total values of coins are 840. Then

find the total number of coins ​

Answer 1

Gɪᴠᴇɴ :-

• a bag contains 25p coins, 50p coins and 1 rupee coins .
• Ratio of coins = 8 : 4 : 2
• Total value of coins = Rs.840 .

Tᴏ Fɪɴᴅ :-

• the total number of coins ?

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume That, in bag , their was 8x coins of 25p , 4x coins of 50p & 2x coins of 1 Rs.

Than,

→ 8x * (25p) + 4x * (50p) + 2x * 1 = 840

→ 8x * (25/100) + 4x * (50/100) + 2x = 840

→ 8x * (1/4) + 4x * (1/2) + 2x = 840

→ 2x + 2x + 2x = 840

→ 6x = 840

→ x = 140 .

Hence,

→ Total coins = (8x + 4x + 2x) = 14x = 14*140 = 1960 (Ans.)

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Verification :-

→ 8x coins of 25p = 8 * 140 * (1/4) = Rs.280

→ 4x coins of 50p = 4 * 140 * (1/2) = Rs.280

→ 2x coins of 1Rs. = 2 * 140 * 1 = Rs.280

Total Amount = 280 + 280 + 280 = Rs.840 (Verified).

_______________________

Now if Given Ratio is of Value of Money , Than :-

Let Value of 25p , 50p & Rs.1 is 8x , 4x & 2x.

→ Total value = 8x + 4x + 2x = 14x

So,

→ 14x = 840

→ x = Rs.60

Therefore,

→ Value of 25p = 8x = 8*60 = Rs.480

→ value of 50p = 4x = 4*60 = Rs.240

→ value of Rs.1 = 2x = 2*60 = Rs.120

Hence,

→ Total Coins of 25p = 480 * 4 = 1920

→ Total Coins of 50p = 240 * 2 = 480

→ Total Coins of Rs.1 = 120 * 1 = 120

→ Total number of coins = 1920+480+120 = 2520 coins (Ans.)

________________________

Answer 2

Answer:-

Let the Values of 25 P coins , 50 P , Rs. 1 coins be 8x , 4x , 2x and number of 25P coins be 25a , 50 P coins be 50b and 100 P (Rs. 1) Coins be 100c.

According to the question,

8x + 4x + 2x = 840

→ 14x = 840

→ x = 840/14

→ x = Rs. 60

Hence,

Value of 25 P coins = 8*60 = Rs. 480

→ 25a = 480 * 100 P

→ a = 480*100/25

→ a = 1920

→ Number of 25 P coins ( a ) = 1920

Value of 50 P coins = 4 * 60 = Rs. 240

→ 50b = 240* 100 P

→ b = 240*100/50

→ b = 480

→ Number of 50 P coins = 480

Value of 100 P coins = 2* 60 = Rs. 120

→ 100c = 120 * 100

→ c = 120 * 100/100

→ c = 120

→ Number of Rs. 1 Coins = 120

Total number of coins = 1920 + 480 + 120 = 2520.

Therefore, there are 2520 coins in the bag.