# Question

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 .

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)

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Why 8u – 4u = 2/5 ?

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-8u -4u can you exp that step how u got

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

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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.

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