Which two numbers (not digits) should be interchanged to make the given equation correct? 24 ÷ 3 – 4 × 2 + 6 × 5 + 12 = 50

Question

UPSC Quizroom · Accepted Answer

Original equation:

24 ÷ 3 – 4 × 2 + 6 × 5 + 12

Let’s evaluate the original first:

24 ÷ 3 = 8
8 – 4×2 + 6×5 + 12
4×2 = 8
6×5 = 30

So:
8 – 8 + 30 + 12 = 42 (not 50)

Now test each option.

Option (1): interchange 5 and 4

Equation becomes:

24 ÷ 3 – 5 × 2 + 6 × 4 + 12
= 8 – 10 + 24 + 12
= 34 (≠ 50)

❌ Not correct

Option (2): interchange 4 and 3

Equation becomes:

24 ÷ 4 – 3 × 2 + 6 × 5 + 12
24 ÷ 4 = 6
3×2 = 6

So:
6 – 6 + 30 + 12 = 42 (≠ 50)

❌ Not correct

Option (3): interchange 24 and 12

Equation becomes:

12 ÷ 3 – 4 × 2 + 6 × 5 + 24
12 ÷ 3 = 4
4×2 = 8
6×5 = 30

So:
4 – 8 + 30 + 24
= -4 + 54
= 50

✔ This works!

Option (4): interchange 3 and 2

Equation becomes:

24 ÷ 2 – 4 × 3 + 6 × 5 + 12
24 ÷ 2 = 12
4×3 = 12

12 – 12 + 30 + 12 = 42 (≠ 50)

❌ Not correct

✅ Correct Answer: (3) 24 and 12

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