15. The volume of water in bottle P was 3/5 of that in bottle Q. After 60 ml of water was added to bottle P and 20 ml was poured away from bottle Q, the amount of water in bottle P was 3/4 that in bottle Q. What was the amount of water in each bottle at first?
60 ÷ 3 = 20
20 x 4 = 80
P [ ][ ][ ] [ 60 ]
Q [ ][ ][ ][ ][ ]
[ 80 ][20]
[ 80 ][20]
1 u --> 80 + 20 = 100
or
P [ ][ ][ ][ 60 ]
Q [ ][ ][ ][ ][ ]
[ ][20][ ][20][ ][20][ ][20][20]
1 u --> 5 x 20 = 100
P: 3 u --> 3 x 100 = 300 ml
Q: 5 u --> 5 x 100 = 500 ml
The amount of water in P was 300 ml and the amount of water in Q was 500 ml.
Alternative method
P Q
x 4 x 3
----------------------------------------------
12 3 : 5 15
+ 240 + 60 - 20 - 60
----------------------------------------------
12 3 : 4 12
----------------------------------------------
12 u + 240 -- > 15 u – 60
3 u -- > 240 + 60 = 300
1 u -- > 300 ÷ 3 = 100
P: 3 u --> 3 x 100 = 300 ml
Q: 5 u --> 5 x 100 = 500 ml
The amount of water in P was 300 ml and the amount of water in Q was 500 ml.
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