Answer:
a) x = 36%
b) c = 52.2
c) z =38%
d) y = 16%
Step-by-step explanation:
a) Given that b is x% more than a and c is y% more than b.
Therefore, [tex]a(1 + \frac{x}{100}) = b[/tex] ....... (1)
Now, if a = 25.25 and b = 34.34, then from equation (1) we get,
[tex]25.25 (1 + \frac{x}{100}) = 34.34[/tex]
⇒ x = 36% (Answer)
b) Given that b is x% more than a and c is y% more than b.
So, [tex]a(1 + \frac{x}{100}) = b[/tex] ......... (2)
and, [tex]b(1 + \frac{y}{100}) = c[/tex] ......... (3)
If a = 36 and x = 25%, then from equation (2) we gat,
[tex]b = 36(1 + \frac{25}{100})[/tex]
⇒ b = 45
Now, y = 16%, then from equation (3) we get
[tex]c = 45(1 + \frac{16}{100})[/tex]
⇒ c = 52.2 (Answer)
c) Given that b is x% more than a and c is y% more than b. And c is z% more than a.
Now, if x = 15% and y = 20%, then
[tex]b = a(1 + \frac{15}{100}) = 1.15a[/tex] and [tex]c = b(1 + \frac{20}{100}) = 1.2b[/tex]
⇒ c = 1.2(1.15a) = 1.38a
Therefore, [tex]a(1 + \frac{z}{100}) = c = 1.38a[/tex]
⇒ z =38% (Answer)
d) Given that b is x% more than a and c is y% more than b. And c is z% more than a.
If x = 25% and z = 45%, then
[tex]b = a(1 + \frac{25}{100}) = 1.25a[/tex] and
[tex]c = b(1 + \frac{y}{100}) = 1.25a(1 + \frac{y}{100})[/tex] ........... (4) and
[tex]c = a(1 + \frac{45}{100}) = 1.45a[/tex] ......... (5)
Now, from equations (4) and (5) we get
[tex]1.25a(1 + \frac{y}{100}) = 1.45a[/tex]
⇒ y = 16% (Answer)
