Question : Directions: Which two digits and signs can be interchanged to balance the given equation?
25 – 9 + 42 ÷ 6 × 7 = 17
Option 1: 9 and 6; + and ×
Option 2: 2 and 5; ÷ and ×
Option 3: 5 and 7; – and ÷
Option 4: 4 and 6; + and ÷
Correct Answer: 5 and 7; – and ÷
Solution :
Given:
25 – 9 + 42 ÷ 6 × 7 = 17
Let's check each option –
First option:
9 and 6, + and ×
On interchanging the mathematical signs and digits, we get –
25 – 6 × 42 ÷ 9 + 7 = 17
On solving the L.H.S. of the equation –
= 25 – 6 × 42 ÷ 9 + 7
= 25 – 28 + 7
= 4
≠
17
Second Option:
2 and 5, ÷ and ×
On interchanging the mathematical signs and digits, we get –
52 – 9 + 42 × 6 ÷ 7 = 17
On solving the L.H.S. of the equation –
= 52 – 9 + 42 × 6 ÷ 7
= 52 – 9 + 36
= 79
≠
17
Third Option:
5 and 7, – and ÷
On interchanging the mathematical signs and digits, we get –
27 ÷ 9 + 42 – 6 × 5 = 15
On solving the L.H.S. of the equation –
= 27 ÷ 9 + 42 – 6 × 5
= 3 + 42 – 6 × 5
= 3 + 42 – 30
= 15
Fourth option:
4 and 6, + and ÷
On interchanging the mathematical signs and digits, we get –
25 – 9 ÷ 62 + 4 × 7 = 17
On solving the L.H.S. of the equation –
= 25 – 9 ÷ 62 + 4 × 7
= 25 – 0.145 + 4 × 7
= 25 – 0.145 + 28
= 52.855
≠
17
So, only the third option satisfies the equation. Hence, the third option is correct.
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