Nick had 2 identical containers. One container was completely filled with water. The other container was 5/9 filled with syrup. He used some water and some syrup to make a drink . He had the same amount of water and syrup left. He used 2/5 l more water than syrup. How much syrup did he have at first ? Give your answer as a fraction in its simplest form .
ConceptualMaths
W : S
At first 9 : 5
-8u | | -4u
In the end 1 : 1
8u – 4u = 2/5
4u = 2/5
1u = 2/5 ÷ 4
= 2/5 × 1/4
= 1/10
Amt of syrup at first = 5u
= 5 × 1/10 litres
= 1/2 litres (ans)
Why 8u – 4u = 2/5 ?
-8u -4u can you exp that step how u got
ConceptualMaths
Because there were equal amount of water and syrup in the end, so W : S would be 1 : 1. Comparing the at first ratio and in the end ratio, the change in unit for each would be the units used.
So water –> 9u-1u=8u
Syrup –> 5u-1u=4u
amount of water at first : 9 units
amount of water used : 1p
amount of syrup at first : 5 units
amount of syrup used : 1p + 2/5
9 units – 1p = 5 units – (1p + 2/5)
1 unit = (2/5)/(9 – 5) = 1/10
5 units = 5/10 = 1/2
Ans : 1/2 l.
