9. IfA: B = B:C=C:D=D: E and A: D = 64
125, then find
(i) A: E = ?
(a) 110:55
(b) 420:221
(c) 256: 625
(d) 220 : 110
Answers
Answer:
A:E = 256:625
Step-by-step explanation:
Hope it helps you
Answer:
A:E = 256:625, B:E = 64:125 and C:E = 16:25.
Step-by-step explanation:
We have,
A:B = B:C = C:D = D:E = x (say)
Also,
A:D = 64:125
So,
On multiplying the terms with each other we get,
\begin{gathered}\frac{A}{B} \times \frac{B}{C} \times \frac{C}{D} = x \times x \times x = x^{3}\\ \\\frac{A}{D} = \frac{64}{125} = x^{3}\\\\So,\\x = \frac{4}{5}\end{gathered}
B
A
×
C
B
×
D
C
=x×x×x=x
3
D
A
=
125
64
=x
3
So,
x=
5
4
So,
\frac{A}{B} \times \frac{B}{C} \times \frac{C}{D} \times \frac{D}{E}=\frac{A}{E}=x^{4}=(\frac{4}{5} )^{4}=\frac{256}{625}
B
A
×
C
B
×
D
C
×
E
D
=
E
A
=x
4
=(
5
4
)
4
=
625
256
Now,
\begin{gathered}\frac{B}{C} \times \frac{C}{D}\times \frac{D}{E} = \frac{B}{E} = x^{3} = (\frac{4}{5} )^{3} = \frac{64}{125}\\also,\\\frac{C}{D}\times \frac{D}{E}=\frac{C}{E}=x^{2}=(\frac{4}{5} )^{2}=\frac{16}{25}\end{gathered}
C
B
×
D
C
×
E
D
=
E
B
=x
3
=(
5
4
)
3
=
125
64
also,
D
C
×
E
D
=
E
C
=x
2
=(
5
4
)
2
=
25
16
Therefore, the value of A:E = 256:625, B:E = 64:125 and C:E = 16:25.