There were some mangoes at a shop. In the morning, ¹₅ of mangoes were sold. In the afternoon, another 28 mangoes were sold. The total number of mangoes left was 5 less than ⁵₁₂ of the number of mangoes the shop had at first.

1. How many mangoes were there at first?
2. What fraction of the mangoes in the shop remained unsold in the afternoon?

	Comparison 1	Comparison 2
Before	5x12 =  60 u	12x5 =  60 u
Change 1	- 1x12 = - 12 u
After 1	4x12 =  48 u
Change 2	- 28
After 2	48 u - 28	5x5 - 5 = 25 u - 5

(a)
The number of mangoes at first is repeated in both comparisons. Make the number of mangoes at first.  LCM of 5 and 12 is 60.

The number of mangoes in the end is the same in both comparisons.

48 u - 28 = 25 u - 5
48 u - 25 u = 28 - 5
23 u = 23

1 u = 23 ÷ 23 = 1

Number of mangoes at first
= 60 u
= 60 x 1
= 60

(b)
Number of mangoes that remained unsold
= 48 u - 28
= 48 x 1 - 28
= 48 - 28
= 20

Fraction of mangoes that remained unsold
= ²⁰₆₀
= ¹₃

Answer(s): (a) 60; (b) ¹₃