Question : Directions: Which of the following interchange of numbers and signs would make the given equation correct?
24 × 9 + 6 ÷ 24 – 18 = 22
Option 1: 18 and 22, + and –
Option 2: 24 and 6, × and +
Option 3: 6 and 9, ÷ and +
Option 4: 6 and 18, ÷ and ×
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Correct Answer: 6 and 9, ÷ and +
Solution :
Given:
24 × 9 + 6 ÷ 24 – 18 = 22
Let's check the given options –
First option:
18 and 22, + and –
⇒ 24 × 9 – 6 ÷ 24 + 22 = 18
Solving the L.H.S. of the equation –
= 24 × 9 – 0.25 + 22
= 216 – 0.25 + 22
= 238 – 0.25
= 237.75
≠
18
Second option:
24 and 6, × and +
Since there are two 24s in the equation, it is unclear which 24 should be replaced by 6. So, this option is incorrect.
Third option:
6 and 9, ÷ and +
⇒ 24 × 6 ÷ 9 + 24 – 18 = 22
Solving the L.H.S. of the equation –
=
24 × 6 ÷ 9 + 24 – 18
= 16 + 24 – 18
= 40 – 18
= 22 = R.H.S.
Fourth option:
6 and 18, ÷ and ×
⇒ 24 ÷ 9 + 18 × 24 – 6 = 22
Solving the L.H.S. of the equation –
=
24 ÷ 9 + 18 × 24 – 6
= 2.67 + 18 × 24 – 6
= 2.67 + 432 – 6
= 434.67 – 6
= 428.67
≠ 22
So, only the third option satisfies the given equation. Hence, the third option is correct.
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