Answer:
A) For the ratio 2:5:13, we can write:
2x + 5x + 13x = 192
Simplifying, we get:
20x = 192
x = 9.6
Therefore, the amounts received by the three people are:
2x = 19.2
5x = 48
13x = 124.8
The smallest share is 19.2 and the largest share is 124.8. Hence, the difference between the largest share and the smallest share is:
124.8 - 19.2 = 105.6
Therefore, the difference between the largest share and the smallest share is 105.6.
B) For the ratio 22:5:14, we can write:
22x + 5x + 14x = 192
Simplifying, we get:
41x = 192
x = 4.68
Therefore, the amounts received by the three people are:
22x = 102.96
5x = 23.4
14x = 65.52
The smallest share is 23.4 and the largest share is 102.96. Hence, the difference between the largest share and the smallest share is:
102.96 - 23.4 = 79.56
Therefore, the difference between the largest share and the smallest share is 79.56.