NIMCET 2007 — Reasoning PYQ

1. Understanding the Decoder Key

First, let's map out the given changes to the mathematical operators based on the problem statement:

• $+\to ÷$

• $-\to \times$

• $÷\to -$

• $\times \to +$

2. Substituting the Signs

Now, replace the original signs in the given expression with their new assigned meanings:

Original Expression:

$$10-14\times 8+2÷16+8$$

New Decoded Expression:

$$10\times 14+8÷2-16÷8$$

3. Solving Using BODMAS / VBODMAS Rule

To evaluate the decoded expression correctly, we follow the standard order of operations (Brackets, Of, Division, Multiplication, Addition, Subtraction):

• Step 1: Division ($÷$)

  Perform the division operations first.

  $$8÷2=4$$

  $$16÷8=2$$

  Substitute these values back into the expression:

  $$10\times 14+4-2$$

• Step 2: Multiplication ($\times$)

  Next, perform the multiplication operation.

  $$10\times 14=140$$

  Substitute this value back into the expression:

  $$140+4-2$$

• Step 3: Addition ($+$) and Subtraction ($-$ )

  Finally, complete the remaining addition and subtraction from left to right.

  $$140+4=144$$

  $$144-2=142$$

Final Answer

The final calculated value is $142$.

Therefore, the correct option is (a).