A safe contains coins of 50 paise, 25 paise and 10 paise. There is a 2:3 ratio between the number of coins of 50 paise and 25 paise and the same ratio is there between the number of 25 paise and 10 paise coins. If total money in the safe is rupees 660, find the number of each type of coins. [Ans. 50 paise coins 60, 25 paise coins 90, 10 paise coins 135]
Answers
Answer:
The number of 50 paise coins = 600
The number of 25 paise coins = 900
The number of 10 paise coins = 1350
Step-by-step explanation:
Solution :-
Given that
A safe contains coins of 50 paise, 25 paise and 10 paise.
The ratio of the number of coins of 50 paise and the number of 25 paise of coins = 2:3
and the number of 25 paise of coins and
the number of 10 paise of coins = 2:3
50 paise coins : 25 paise coins = 2:3
on multiplying with 2 then
50 paise coins : 25 paise coins = 4:6 ---(1)
and
25 paise coins : 10 paise coins = 2:3
on multiplying with 3 then
25 paise coins : 10 paise coins = 6:9 ----(2)
From (1) & (2) we get
50 paise coins : 25 paise coins : 10 piase coins
= 4:6:9
Let they be 4X , 6X and 9X
The number of 50 paise coins = 4X
We know that
1 Rupee = 100 paise
50 paise = 50/100 = Rs. 1/2
Value of all 50 paise coins = (1/2)×4X
= Rs. 2X
The number of 25 paise coins = 6X
Value of all 25 paise coins = (1/4)×6X
= Rs. 3X/2
Since , 25 paise = 25/100 = Rs. 1/4
The number of 10 paise coins = 9X
Value of all 10 paise coins = (1/10)×9X
= Rs. 9X/10
Since , 10 paise = 10/100 = Rs. 1/10
Total amount in the safe
= 2X + (3X/2) + (9X/10)
LCM of 2 and 10 = 10
= [(10×2X)+(5×3X)+(9X)]/10
= (20X+15X+9X)/10
= 44X/10
= Rs. 22X/5
According to the given problem
The total money in the safe = Rs. 660
=> 22X/5 = 660
=> 22X = 660×5
=> 22X = 3300
=> X = 3300/22
=> X = 300/2
=> X = 150
Now,
If X = 150 then 4X = 4(150) = 600
The number of 50 paise coins = 600
If X = 150 then 6X = 6(150) = 900
The number of 25 paise coins = 900
If X = 150 then 9X = 9(150) = 1350
The number of 10 paise coins = 1350
Answer :-
The number of 50 paise coins = 600
The number of 25 paise coins = 900
The number of 10 paise coins = 1350
Check :-
The number of 50 paise coins = 600
The number of 25 paise coins = 900
The number of 10 paise coins = 1350
The ratio of the number of 50 paise coins and the number of 25 paise coins
= 600:900
= (2×300):(3×300)
= 2:3
The ratio of the number of 25 paise coins and the number of 10 paise coins
= 900 :1350
= (2×450):(3×450)
= 2:3
Therefore,
There is a 2:3 ratio between the number of coins of 50 paise and 25 paise and the same ratio is there between the number of 25 paise and 10 paise coins.
and
Value of 50 paise coins
= 600×50 paise
= 30000 paise
=Rs. 30000/100
= Rs. 300
Value of 25 paise coins
= 900×25 paise
= 22500 paise
= Rs. 22500/100
= Rs. 225
Value of 10 paise coins
= 1350×10 paise
= 13500 paise
= Rs. 13500/100
= Rs. 135
Total money in the safe
= 300 + 225 + 135
= Rs. 660
= Given amount in the problem
Verified the given relations in the given problem.
Note :-
Given answer in the question is wrong because
If the number of 50 paise coins is 60 then the value of the coins
= 60×1/2
= Rs. 30
If the number of 25 paise coins is 90 then the value of the coins
= 60×1/4
= Rs. 15
If the number of 10 paise coins is 135 then the value of the coins
= 135×1/10
= Rs. 13.50
Total money in the safe
= 30+15+13.50
= Rs. 58.50
But given money is Rs. 660.
Step-by-step explanation:
Answer:
Given that
A safe contains coins of 50 paise, 25 paise and 10 paise.
The ratio of the number of coins of 50 paise and the number of 25 paise of coins = 2:3
and the number of 25 paise of coins and
the number of 10 paise of coins = 2:3
50 paise coins : 25 paise coins = 2:3
on multiplying with 2 then
50 paise coins : 25 paise coins = 4:6 ---(1)
and
25 paise coins : 10 paise coins = 2:3
on multiplying with 3 then
25 paise coins : 10 paise coins = 6:9 ----(2)
From (1) & (2) we get
50 paise coins : 25 paise coins : 10 piase coins
= 4:6:9
Let they be 4X , 6X and 9X
The number of 50 paise coins = 4X
We know that
1 Rupee = 100 paise
50 paise = 50/100 = Rs. 1/2
Value of all 50 paise coins = (1/2)×4X
= Rs. 2X
The number of 25 paise coins = 6X
Value of all 25 paise coins = (1/4)×6X
= Rs. 3X/2
Since , 25 paise = 25/100 = Rs. 1/4
The number of 10 paise coins = 9X
Value of all 10 paise coins = (1/10)×9X
= Rs. 9X/10
Since , 10 paise = 10/100 = Rs. 1/10
Total amount in the safe
= 2X + (3X/2) + (9X/10)
LCM of 2 and 10 = 10
= [(10×2X)+(5×3X)+(9X)]/10
= (20X+15X+9X)/10
= 44X/10
= Rs. 22X/5
According to the given problem
The total money in the safe = Rs. 660
=> 22X/5 = 660
=> 22X = 660×5
=> 22X = 3300
=> X = 3300/22
=> X = 300/2
=> X = 150
Now,
If X = 150 then 4X = 4(150) = 600
The number of 50 paise coins = 600
If X = 150 then 6X = 6(150) = 900
The number of 25 paise coins = 900
If X = 150 then 9X = 9(150) = 1350
The number of 10 paise coins = 1350
Answer :-
The number of 50 paise coins = 600
The number of 25 paise coins = 900
The number of 10 paise coins = 1350
Check :-
The number of 50 paise coins = 600
The number of 25 paise coins = 900
The number of 10 paise coins = 1350
The ratio of the number of 50 paise coins and the number of 25 paise coins
= 600:900
= (2×300):(3×300)
= 2:3
The ratio of the number of 25 paise coins and the number of 10 paise coins
= 900 :1350
= (2×450):(3×450)
= 2:3
Therefore,
There is a 2:3 ratio between the number of coins of 50 paise and 25 paise and the same ratio is there between the number of 25 paise and 10 paise coins.
and
Value of 50 paise coins
= 600×50 paise
= 30000 paise
=Rs. 30000/100
= Rs. 300
Value of 25 paise coins
= 900×25 paise
= 22500 paise
= Rs. 22500/100
= Rs. 225
Value of 10 paise coins
= 1350×10 paise
= 13500 paise
= Rs. 13500/100
= Rs. 135
Total money in the safe
= 300 + 225 + 135
= Rs. 660
= Given amount in the problem
Verified the given relations in the given problem.
Note :-
Given answer in the question is wrong because
If the number of 50 paise coins is 60 then the value of the coins
= 60×1/2
= Rs. 30
If the number of 25 paise coins is 90 then the value of the coins
= 60×1/4
= Rs. 15
If the number of 10 paise coins is 135 then the value of the coins
= 135×1/10
= Rs. 13.50
Total money in the safe
= 30+15+13.50
= Rs. 58.50
But given money is Rs. 660.