Linda purchased a bottle of mangosteen syrup to make drinks. She used ³₅ of the syrup in January. She then used the remaining syrup in February and March in the ratio 1 : 10. Given that the amount of the mangosteen syrup used in January was 1.24 ℓ more than that in February, how many millilitres of mangosteen syrup did the bottle contain at first?

January	February	March	Total
3x11	2x11		5x11
	1x2	10x2
33 u	2 u	20 u	55 u

Total volume of February and March is combined repeated identity.  Make the total volume of February and March the same.  LCM of 2 and 11 is 22.

Volume of more mangosteen syrup in the bottle used in January than February
= 33 u - 2 u
= 31 u

31 u = 1.24 

1 u = 1.24 ÷ 31 = 0.04

Amount of mangosteen syrup in the bottle at first
= 55 u
= 55 x 0.04
= 2.2 ℓ

1 ℓ = 1000 mℓ

Amount of mangosteen syrup in the bottle at first
= 2.2 x 1000
= 2200 mℓ

Answer(s): 2200 mℓ