Question : Directions: Which of the following interchange of numbers and signs would make the given equation correct?
10 − 4 ÷ 20 + 16 × 8 = 16
Option 1: 10 and 16, × and ÷
Option 2: 4 and 8, × and −
Option 3: 4 and 20, + and ÷
Option 4: 10 and 20, + and ×
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Correct Answer: 4 and 8, × and −
Solution :
Given:
10 − 4 ÷ 20 + 16 × 8 = 16
Let's check the given options –
First option:
10 and 16, × and ÷
Since there are two 16s in the equation, it is not clear which 16 needs to be interchanged. So, this option is incorrect.
Second option:
4 and 8, × and −
On interchanging the signs and numbers, we get –
⇒ 10 × 8 ÷ 20 + 16 – 4 = 16
Solving the L.H.S. of the equation –
= 10 × 0.4 + 16 – 4
= 4 + 16 − 4
= 16
Third option:
4 and 20, + and ÷
On interchanging the signs and numbers, we get –
⇒ 10 − 20 + 4 ÷ 16 × 8 = 16
Solving the L.H.S. of the equation –
= 10 − 20 + 0.25 × 8
= 10 – 20 + 2
= 12 – 20
= –8 ≠ 16
Fourth option:
10 and 20, + and ×
On interchanging the signs and numbers, we get –
⇒ 20 − 4 ÷ 10 × 16 + 8 = 16
Solving the L.H.S. of the equation –
= 20 − 0.4 × 16 + 8
= 20 − 2.4 + 8
= 28 – 2.4
= 25.6 ≠ 16
So, only the second option satisfies the given equation. Hence, the second option is correct.
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