Question : Directions: Which of the following interchanges of signs would make the given equation correct?
100 + 100 × 50 – 2 ÷ 3 = 51
Option 1: + and ÷
Option 2: + and –
Option 3: – and ×
Option 4: ÷ and ×
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Correct Answer: + and ÷
Solution :
Given:
100 + 100 × 50 – 2 ÷ 3 = 51
On interchanging the mathematical signs as directed in the options –
First option:
+ and ÷
⇒ 100 ÷ 100 × 50 – 2 + 3 = 51
Solving the L.H.S. of the given equation –
= 1 × 50 – 2 + 3
= 50 – 2 + 3
= 53 – 2
= 51 = R.H.S.
Second option:
+ and –
⇒ 100 – 100 × 50 + 2 ÷ 3 = 51
Solving the L.H.S. of the given equation –
= 100 – 100 × 50 + 0.67 = 51
= 100 – 5000 + 0.67
= 100.67 – 5000
= –4899.33 ≠ 51
Third option:
– and ×
⇒ 100 + 100 – 50 × 2 ÷ 3 = 51
Solving the L.H.S. of the given equation –
= 100 + 100 – 50 × 0.67
= 100 + 100 – 33.5
= 200 – 33.5
= 166.5 ≠ 51
Fourth option:
÷ and ×
⇒ 100 + 100 ÷ 50 – 2 × 3 = 51
Solving the L.H.S. of the given equation –
= 100 + 2 – 2 × 3
= 100 + 2 – 6
= 102 – 6
= 96 ≠ 51
So, only the first option satisfies the R.H.S. of the given equation. Hence, the first option is correct.
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