Question : Directions: Which of the following interchange of numbers and mathematical signs would make the given equation correct?
72 ÷ 8 × 9 − 36 + 20 = 80
Option 1: 20 and 80, × and +
Option 2: 9 and 36, × and ÷
Option 3: 36 and 72, ÷ and −
Option 4: 8 and 9, + and −
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Correct Answer: 8 and 9, + and −
Solution :
Given:
72 ÷ 8 × 9 − 36 + 20 = 80
Let's check the given options –
First option:
20 and 80, × and +
On interchanging the signs and numbers, we get –
⇒ 72 ÷ 8 + 9 − 36 × 80 = 20
Solving the L.H.S. of the equation –
= 72 ÷ 8 + 9 − 36 × 80
= 9 + 9 − 36 × 80
= 9 + 9 − 2880
= 18 − 2880
= −2862 ≠ 20
Second option:
9 and 36, × and ÷
On interchanging the signs and numbers, we get –
⇒ 72 × 8 ÷ 36 − 9 + 20 = 80
Solving the L.H.S. of the equation –
= 72 × 8 ÷ 36 − 9 + 20
= 16 − 9 + 20
= 36 – 9
= 27 ≠ 80
Third option:
36 and 72, ÷ and −
⇒ 36 – 8 × 9 ÷ 72 + 20 = 80
Solving the L.H.S. of the equation –
= 36 – 8 × 9 ÷ 72 + 20
= 36 – 8 × 0.125 + 20
= 36 – 1 + 20
= 56 – 1
= 55 ≠ 80
Fourth option:
8 and 9, + and −
⇒ 72 ÷ 9 × 8 + 36 – 20 = 80
Solving the L.H.S. of the equation –
= 72 ÷ 9 × 8 + 36 – 20
= 8 × 8 + 36 – 20
= 64 + 36 – 20
= 100 – 20
= 80
So, only the fourth option satisfies the given equation. Hence, the fourth option is correct.
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