Rachel purchased a bottle of detergent. She used ³₅ of the detergent in April. She then used the remaining detergent in May and June in the ratio 3 : 4. Given that the amount of the detergent used in June was 0.52 ℓ less than that in April, how many millilitres of detergent did the bottle contain at first?

April	May	June	Total
3x7	2x7		5x7
	3x2	4x2
21 u	6 u	8 u	35 u

Total volume of May and June is combined repeated identity. Make the total volume of May and June the same. LCM of 2 and 7 is 14.

Volume of less detergent syrup in the bottle used in June than April
= 21 u - 8 u
= 13 u

13 u = 0.52 

1 u = 0.52 ÷ 13 = 0.04

Amount of detergent in the bottle at first
= 35 u
= 35 x 0.04
= 1.4 ℓ

1 ℓ = 1000 mℓ

Amount of detergent in the bottle at first
= 1.4 x 1000
= 1400 mℓ

Answer(s): 1400 mℓ