Question

IF. A : B = 2 : 3. B : C = 4 : 5. C : D = 5 : 8 THE VALUE OF A : D ​

Answer 1

the answer

A/B*B/C*C/D

=2/3*4/5*5/8

=3

IS CORRECT ANSWER

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Answer 2

Answer:

• A : D = 1 : 3

Step-by-step explanation:

Given that:

• A : B = 2 : 3
• B : C = 4 : 5
• C : D = 5 : 8

To Find:

• Value of A : D.

Solution:

As we know that,

$\sf{\circ\;\dfrac{A}{B}=\dfrac{2}{3}}$

$\sf{\circ\;\dfrac{B}{C}=\dfrac{4}{5}}$

$\sf{\circ\;\dfrac{C}{D}=\dfrac{5}{8}}$

As, in A/B and B/C the value of B is not same so, we have to take the LCM of 3 and 4 to make the values same.

∵ LCM of 3 and 4 = 3 × 4 = 12.

Therefore,

$\sf{\circ\;\dfrac{A}{B}=\dfrac{2\times4}{3\times4}=\dfrac{8}{12}}$

$\sf{\circ\;\dfrac{B}{C}=\dfrac{4\times3}{5\times3}=\dfrac{12}{15}}$

Hence,

$\sf{\circ\;\dfrac{A}{B}=\dfrac{8}{12}}$

$\sf{\circ\;\dfrac{B}{C}=\dfrac{12}{15}}$

Now, in B/C and C/D the value of C is not same so, we have to take the LCM of 15 and 5 to make the values same.

∵ LCM of 15 and 5 = 15.

Therefore,

$\sf{\circ\;\dfrac{B}{C}=\dfrac{12\times1}{15\times1}=\dfrac{12}{15}}$

$\sf{\circ\;\dfrac{C}{D}=\dfrac{5\times3}{8\times3}=\dfrac{15}{24}}$

Hence,

$\sf{\circ\;\dfrac{A}{B}=\dfrac{8}{12}}$

$\sf{\circ\;\dfrac{B}{C}=\dfrac{12}{15}}$

Now, finding A : D,

$\sf{\dfrac{A}{D}=\dfrac{A}{B}\times\dfrac{B}{C}\times\dfrac{C}{D}}$

Substituting the values,

$\sf{\longmapsto\dfrac{8}{12}\times\dfrac{12}{15}\times\dfrac{15}{24}}$

Cutting off the numbers,

$\sf{\longmapsto\dfrac{8}{\!\!\!\not{1}\!\!\!\not{2}}\times\;\dfrac{\!\!\!\not{1}\!\!\!\not{2}}{\!\!\!\not{1}\!\!\!\not{5}}\times\;\dfrac{\!\!\!\not{1}\!\!\!\not{5}}{24}}$

$\sf{\longmapsto\dfrac{8}{24}}$

Reducing the numbers,

$\sf{\longmapsto\dfrac{8\div8}{24\div8}}$

$\sf{\longmapsto\dfrac{1}{3}}$

Hence,

• A : D = 1 : 3