Question : Directions: Which two signs and two numbers should be interchanged in the following equation to make it correct?
15 ÷ 80 – 34 + 10 × 8 = 102
Option 1: 10, 80, ÷, –
Option 2: 15, 34, –, ×
Option 3: 34, 15, +, ÷
Option 4: 10, 34, ÷, ×
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Correct Answer: 34, 15, +, ÷
Solution :
Given:
15 ÷ 80 – 34 + 10 × 8 = 102
Replace the given symbols in the options one by one with the original symbols in the given equation.
First option:
10, 80, ÷, –
The equation becomes ⇒ 15 – 10 ÷ 34 + 80 × 8 = 102
Solving the L.H.S. of the equation –
= 15 – 10 ÷ 34 + 80 × 8
= 15 – 0.29 + 640
= 654.71 ≠ 102
Second option:
15, 34, –, ×
The equation becomes ⇒ 34 ÷ 80 × 15 + 10 – 8 = 102
Solving the L.H.S. of the equation –
= 34 ÷ 80 × 15 + 10 – 8
= 0.425 × 15 + 10 – 8
= 6.375 + 10 – 8
= 8.375 ≠ 102
Third option:
34, 15, +, ÷
The equation becomes ⇒ 34 + 80 – 15 ÷ 10 × 8 = 102
Solving the L.H.S. of the equation –
= 34 + 80 – 15 ÷ 10 × 8
= 34 + 80 – 1.5 × 8
= 34 + 80 – 12
= 102
Fourth option:
10, 34, ÷, ×
The equation becomes ⇒ 15 × 80 – 10 + 34 ÷ 8 = 102
Solving the L.H.S. of the equation –
= 15 × 80 – 10 + 34 ÷ 8
= 1200 – 10 + 4.25
= 1194.25 ≠ 102
So, only the third option satisfies the equation. Hence, the third option is correct.
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