A bag contains 25p, 50p and 1 rupee coins. There are 220 coin in all & the total amount in bag is 160. If there are thrice as many 1 rupee coins as there are 25p coins, then what is the no. of 50 paise coin?
A. 60
B. 40
C. 120
D. 80
Solution (By Examveda Team)
Let No of 25 paise coins are X. Then number of 1 rupee coins are 3x.
Number of 50 paise coins = Y
Total number of coins = 220
Total Amount = Rs. 160.
Now,
0.25X + 0.5Y +3X = 160 ---------------------------- (1)*4
Total Number of coins,
X +3X + Y = 220
4X +Y = 220 ------------------------------------- (2)*2
Now solving equation 1 and equation 2. (equation 1 - equation 2)
X + 2Y + 12X - 8X - 2Y = 640 - 440
5X = 200
X = 40.
Putting the value of X in equation (2)
4 *40 +Y = 220
160 + Y = 220
Y = 60.
Number of coins of 50 paise = 60.
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LET NO OF 25 PAISE COIN IS X THEN NO 100 PAISE COIN WILL BE 3X AS THE NO OF 1RS COIN IS THRICE THAT OF NO OF 25 PAISE COIN
LET NO OF 25 PAISE COIN IS Y
GIVEN : total amount 160
total no of coin is: 220
now for total amount
0.25X+0.5Y+3X=160 EQ 1
SOLVING EQ 1 WE HAVE
13X+2Y=640 EQ 2
EQUATION FOR TOTAL NO OF COIN:
X+3X+Y=220 EQ 3
SOLVING EQ 3
WE HAVE 4X+Y =220 EQ 4
NOW USING EQ (2 & 4)
AND MAKING THEIR COEFFICIENT EQUAL WE WILL GET Y 60
WHICH THE REQUIRED ANS