Question : Directions: Which of the following interchange of numbers and mathematical signs would make the given equation correct?
72 ÷ 6 − 20 + 30 × 5 = 70
Option 1: 5 and 20, − and ×
Option 2: 20 and 30, × and ÷
Option 3: 5 and 70, + and −
Option 4: 6 and 20, + and ÷
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Correct Answer: 5 and 20, − and ×
Solution :
Given:
72 ÷ 6 − 20 + 30 × 5 = 70
Replacing the given numbers and signs in the equation.
First option:
5 and 20, − and ×
72 ÷ 6 × 5 + 30 − 20 = 70
⇒ 12 × 5 + 30 − 20 = 70
= 60 + 30 − 20 = 70
= 90 − 20 = 70
L.H.S = R.H.S
Second option:
20 and 30, × and ÷
72 × 6 − 30 + 20 ÷ 5 = 70
⇒ 72 × 6 − 30 + 4 = 70
= 432 − 30 + 4 = 70
= 432 − 26 = 406 ≠ 70
L.H.S ≠ R.H.S
Third option:
5 and 70, + and −
72 ÷ 6 + 20 − 30 × 70 = 5
⇒ 12 + 20 − 30 × 70 = 5
= 12 + 20 − 2100 = 5
= 12 − 2080 = −2068 ≠ 5
L.H.S ≠ R.H.S
Fourth option:
6 and 20, + and ÷
72 + 20 − 6 ÷ 30 × 5 = 70
⇒ 72 + 20 − 0.2 × 5 = 70
= 72 + 20 − 1 = 70
= 92 − 1 = 91 ≠ 70
L.H.S ≠ R.H.S
So, only the first option satisfies the given equation. Hence, the first option is correct.
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