To make things easier to calculate, treat each bottle as having 7 units of tarts at first.

After repacking, each bottle has 1/7 more tarts than before. This means 1 unit more since 1/7 of 7 units is 1 unit.


As 5 bottles of tarts were emptied,

5 x 7 units = 35 units . So 35 units of tarts were repacked.

35 units ÷ 1 unit = 35. This means they were repacked into 35 remaining bottles, with each of these bottles having 1 unit more tarts than before.

Total number of bottles at first
= 35 + 5 = 40

Number of tarts in each bottle at first
= 1400 ÷ 40
= 35

Shorter working :

Since 5 bottles were emptied and the tarts repacked, and each remaining bottle had 1/7 more tarts,


Number of remaining bottles
= 5 bottles' worth of tarts ÷ 1/7 bottle worth of tarts more per remaining bottle

= 5 x 7/1
(dividing by a fraction = multiplying by the fraction with the numerator and denominator inverted)

= 35

Total bottles at first = 35 + 5 = 40

Tarts per bottle = 1400 ÷ 40 = 35