PSLE
Mrs Lin had a bottle of detergent. She used an equal amount of detergent each day. At the end of the seventh day, she had 1610 mℓ of detergent left. At the end of the tenth day, she had two-thirds of the bottle of detergent left. How many litres of detergent were there in the bottle at first?
Fraction of detergent used after two-thirds of the bottle was left
= 1 - ²₃
= ¹₃

¹₃ of the bottle → 10 days
1 bottle → 10 ÷ ¹₃ = 10 x ³₁ =  30 days

It takes 30 days to finish the whole bottle.

Number of days to use 1610 mℓ of detergent
= 30 - 7
= 23

23 days → 1610 mℓ

1 day → 1610 ÷ 23 = 70 mℓ

30 days → 30 x 70 = 2100 mℓ

1000 mℓ = 1 ℓ

2100 mℓ = 2100 ÷ 1000 = 2.1 ℓ

Volume of detergent in the bottle at first = 2.1 ℓ

Answer(s): 2.1 ℓ