Question : Directions: Which two digits should be interchanged in the given equation to make it mathematically correct?
20 ÷ 7 × 2 + 5 – 3 = 12
Option 1: 2 and 3
Option 2: 7 and 5
Option 3: 7 and 2
Option 4: 2 and 5
Correct Answer: 7 and 5
Solution :
Given:
20 ÷ 7 × 2 + 5 – 3 = 12
Let's check each option –
First Option:
2 and 3
On interchanging the digits, we get –
30 ÷ 7 × 3 + 5 – 2 = 13
On solving the L.H.S. of the equation –
= 30 ÷ 7 × 3 + 5 – 2
= 12.86 + 5 – 2
= 15.86 ≠ 13
Second Option:
7 and 5
On interchanging the digits, we get –
20 ÷ 5 × 2 + 7 – 3 = 12
On solving the L.H.S. of the equation –
= 20 ÷ 5 × 2 + 7 – 3
= 4 × 2 + 7 – 3
= 8 + 7 – 3
= 12
Third Option:
7 and 2
On interchanging the digits, we get –
70 ÷ 2 × 7 + 5 – 3 = 17
On solving the L.H.S. of the equation –
= 70 ÷ 2 × 7 + 5 – 3
= 35 × 7 + 5 – 3
= 245 + 5 – 3
= 247 ≠ 17
Fourth Option:
2 and 5
On interchanging the digits, we get –
50 ÷ 7 × 5 + 2 – 3 = 15
On solving the L.H.S. of the equation –
= 50 ÷ 7 × 5 + 2 – 3
= 35.71 + 2 – 3
= 34.71 ≠ 15
So, only the second option satisfies the equation. Hence, the second option is correct.
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