Question : Directions: Which two numbers from amongst the given options should be interchanged to make the given equation correct?
108 ÷ 3 – 126 ÷ (5 × 3 + 12) + 4 = 11
Option 1: 11 and 12
Option 2: 12 and 3
Option 3: 12 and 4
Option 4: 126 and 108
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Correct Answer: 12 and 3
Solution :
Given:
108 ÷ 3 – 126 ÷ (5 × 3 + 12) + 4 = 11
Interchange the numbers as given in the options.
First option:
11 and 12
After interchanging the numbers the equation becomes –
⇒ 108 ÷ 3 – 126 ÷ (5 × 3 + 11) + 4 = 12
⇒ 108 ÷ 3 – 126 ÷ (26) + 4
⇒ 36 – 4.84 + 4
⇒ 35.16
≠
12
Second option:
12 and 3
After interchanging the numbers the equation becomes –
⇒ 108 ÷ 12 – 126 ÷ (5 × 12 + 3) + 4 = 11
⇒ 108 ÷ 12 – 126 ÷ (63) + 4
⇒ 9 – 2 + 4 = 11
⇒ 11 = 11 (L.H.S. = R.H.S.)
Third option:
12 and 4
After interchanging the numbers the equation becomes –
⇒ 108 ÷ 3 – 126 ÷ (5 × 3 + 4) + 12 = 11
⇒ 108 ÷ 3 – 126 ÷ (19) + 12
⇒ 36 – 6.63 + 12
⇒ 41.37
≠
11
Fourth option:
126 and 108
After interchanging the numbers the equation becomes –
⇒ 126 ÷ 3 – 108 ÷ (5 × 3 + 12) + 4 = 11
⇒ 126 ÷ 3 – 108 ÷ (27) + 4
⇒ 42 – 4 + 4
⇒ 34
≠
11
So, only the second option satisfies the R.H.S. of the equation. Hence, the second option is correct.
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