Sounds a bit like an Independent School entrance exam final scholarship question

Algebraic substitution would be the natural way to work this out with expressions for 1a

Thus

1a=6b (given) substituting for c gives

1a= 6 x 5c/4= 7.5c and for d gives

1a= 7.5x 2d/3= 5d and for e gives

1a=5 x 4e/5= 4e

Hence b=(1/6)a

c= (1/7.5)a

d= (1/5)a

e=(1/4)a

so c is the least (smallest fraction) and 4e=a

It's interesting that I don't think Algebra is in KS2 yet (is that correct G55?) but the scholarship type questions in Independent entrance exams usually require a reason knowledge of Algebra to answer quickly

As an aside, this was the final Maths question in an old Solihull School (Independent) Maths Paper:-**Quote:**

T is a town on the shore of a large lake, and various boats and hovercraft stop at T in their journeys around the lake. The total distance round the lake is 180 kilometres.

At 10:00am a boat starts from T and travels clockwise round the lake at a speed of 15kph. At the same time a hovercroft starts from T and travels round the lake in the opposite direction at 60kpm.

(1) How far has the boat travelled by the time the hovercraft gets back to T?

(2) When do the hovercraft and the boat meet each other?

(3) How far has each vessel travelled when they meet?