Question

The ratio of guppies to angelfish in a shop is 2 : 3. The number of angelfish was 23the number of goldfish. The shopkeeper decided to replace 14of the guppies with some angelfish. The number of angelfish she added was equal to the number of guppies she replaced. There were 30 more goldfish than angelfish in the end. How many guppies were in the shop in the beginning?

Answer 1

The number of guppies were in the shop in the beginning = 60

Explanation:

guppies ⇒ x , angelfish ⇒ y , goldfish ⇒ z

guppies to angelfish = 2 : 3 ⇒ x : y = 2 : 3 ⇒ x = 2/3 y

The number of angelfish was 2/3 the number of goldfish ⇒ y = 2/3 z

Or z = 3/2 y

The shopkeeper decided to replace 1/4 of the guppies with some angelfish. The number of angelfish she added was equal to the number of guppies she replaced

so, the number of guppies = 0.75x

and the number of angelfish = y + 0.25 x = y + 0.25 * 2/3 y

There were 30 more goldfish than angelfish in the end

z - (y + 0.25 * 2/3 y) = 30

so, 3/2 y - (y + 0.25 * 2/3 y) = 30

3/2 y - y - 1/6 y = 30

1/3 y = 30

y = 90

x = 2/3 y =2/3 * 90 = 60

z = 3/2 * 90 = 135

so, the number of guppies were in the shop in the beginning = 60