Question

A question from reasoning

Answer 1

The answer will be
(c) 64
As-
1+1=2&2×4=8
So,16+1=17&17×4=64.
THE PRINCIPLE APPLIED IS —
(X+1)×4.

Answer 2

Answer:

B) 125

Step-by-step explanation:

$\textsf{Here, The question is that if 1:8::16:? and we have to find the question mark.}\\\\\textsf{Let the value to be found be x.}\\\\\textsf{Then, 1:8 may be either in direct proportion or in inverse proportion.}\\\\\text{Considering the question to be in inverse proportion, we have}\\\\\mathsf{1 \times 8 = 16 \times x}\\\\\mathsf{\implies 8 = 16x}\\\\\mathsf{\implies x = 8 \div 16 = 0.5}$

$\textsf{This value is not the the four options of the question. Hence,}\\\textsf{the question is not in inverse proportion. It is in direct proportion.}\\\\\textsf{If it is so, then, we have,}\\\\\mathsf{\dfrac{1}{8} = \dfrac{16}{x}}\\\\\\\mathsf{\implies x = 16 \times 8}\\\\\mathsf{\implies x = \boxed{\boxed{\textsf{128}}}}$

$\textsf{Now, this value is also not in the options. So, we have 2 values now,}\\\textsf{one for inverse proportion case, ie, 0.5 and one for direct proportion case,}\\\textsf{ie, 128. Both the values are not in the four options. But, 128 is closer to 125 but,}\\\textsf{0.5 is not closer to any of the options.}\\\\\textsf{Thus, 125 is the answer.}$

Hope it helps!