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If $A : B = 1 : 2$ , $B : C = 3 : 4$ , and $C : D = 5 : 6$ , then D: A is equal to?

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6:5

5:16

5:6

16:5

answer is D.

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Detailed Solution

Concept- By expressing B and C in terms of A, followed by simple mathematical calculations and cross-multiplications.
Given is that,

\frac{A}{B} = \frac{1}{2}

\frac{B}{C} = \frac{3}{4}

\frac{C}{D} = \frac{5}{6}

Since,

\frac{A}{B} = \frac{1}{2}

By cross-multiplying, we get-

2 A = B

Similarly,

\frac{B}{C} = \frac{3}{4}

∴ 4 B = 3 C

\frac{C}{D} = \frac{5}{6}

∴ 6 C = 5 D

Now from equation (1) and (2):
Putting the value of B from equation (1) into equation (2), we get:

4 B = 3 C

4 \times 2 A = 3 C

8 A = 3 C

Now, equation (3) can be expressed as follows:

6 C = 5 D

2 \times 3 C = 5 D

Putting the value of 3C as 8A from equation (4), we get:

2 \times 8 A = 5 D

16 A = 5 D

\frac{D}{A} = \frac{16}{5}

D : A = 16 : 5

Hence, the correct option is 4) 16 : 5.

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