Question

Note: P6 kids should memorise 25% = 1/4, 50%=1/2, 75% = 3/4,      20% =1/5, 40% = 2/5, 60% = 3/5, 80% = 4/5      at finger-tips and conversion to/from ratio at ease.

If we reword: “If 5 litres of syrup were added, ratio of water to syrup is 3:1” and “if 33 litres of syrup were added, ratio of water to syrup is 2: 5”, then all becomes too familiar…

Water       Syrup      Total

After 5 litres of syrup added     3        :      1         :     4      (x2)

After 33 litres of syrup added   2        :      3        :      5     (x3)

Identify amt of water is unchanged, let it be 6u (I use LCM but can use any number you prefer)

Water       Syrup      Total

After 5 litres of syrup added     6       :            :     8

After 33 litres of syrup added   6      :           :      15

Change in the ratio is due to additional 28 litres of syrup (33-5=28)

change in syrup = 9u – 2u = 15u – 8u =  7u  — > 28 litres

1u  — > 4 litres

2u  — > 8 litres

At first  — > 8 – 5 = 3 litres of syrup#

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Scenario 1 : If 5 litres of syrup were added. 75% of the content in the tank would be water,
syrup : 4u (25%)
water : 12u (75%)

Scenario 2 : If 33 litres of syrup were added. 40% of the content in the tank would be water,
syrup : 18u (60%)
water : 12u (40%)

4u ——- syrup + 5
18u ——- 4.5 x syrup + 22.5
18u ——- syrup + 33
4.5 x syrup + 22.5 ——- syrup + 33
syrup ——- (33 – 22.5)/(4.5 – 1) = 3

Ans : 3 l.

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After adding 5l of S, tank contains 75% W and 25% S.

After adding 33l of S, tank contains 40% W and 60% S.

Assign 75u to be the amount of water in the tank after adding 5l of S.

After adding 5l of S, amount of W in litres in tank is 25u.

After adding 33l of S, amount of W in litres in tank is 60/40 x 75u = 112.5u

112.5u – 25u = 33 – 5

u = 0.32 l

After adding 5l of S, there are 25 x 0.32 =  8l of S in tank.

Before adding, 8-5 = 3l of S.

Check

Initial, 24l of W and 3l of S.

After adding 5l of S, 24l of W and 8l of S. 75% W. Checked.

After adding 33l of S, 24l of W and 36l of S. 40% W. Checked.

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