Question : Directions: Which two numbers from amongst the given options should be interchanged to make the given equation correct?
168 ÷ 4 + 216 ÷ ( 78 × 1 – 8) = 14
Option 1: 78 and 216
Option 2: 14 and 8
Option 3: 78 and 14
Option 4: 216 and 168
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Correct Answer: 78 and 14
Solution :
Given:
168 ÷ 4 + 216 ÷ ( 78 × 1 – 8) = 14
Interchanging the numbers as given in the options –
First option:
78 and 216
168 ÷ 4 + 78 ÷ ( 216 × 1 – 8) = 14
⇒ 168 ÷ 4 + 78 ÷ ( 216 – 8) = 14
⇒ 168 ÷ 4 + 78 ÷ 208 = 14
⇒ 42 + 0.375 = 42.375 ≠ 14
Second option:
14 and 8
168 ÷ 4 + 216 ÷ ( 78 × 1 – 14) = 8
⇒ 168 ÷ 4 + 216 ÷ ( 78 – 14) = 8
⇒ 168 ÷ 4 + 216 ÷ 64 = 8
⇒ 42 + 3.375 = 45.375 ≠ 8
Third option:
78 and 14
168 ÷ 4 + 216 ÷ (14 × 1 – 8) = 78
⇒ 168 ÷ 4 + 216 ÷ (14 – 8) = 78
⇒ 168 ÷ 4 + 216 ÷ 6 = 78
⇒ 42 + 36 = 78
Fourth option:
216 and 168
216 ÷ 4 + 168 ÷ ( 78 × 1 – 8) = 14
⇒ 216 ÷ 4 + 168 ÷ (78 – 8) = 14
⇒ 216 ÷ 4 + 168 ÷ 70 = 14
⇒ 54 + 2.4 = 56.4 ≠ 14
So, only the third option satisfies the R.H.S. of the given equation. Hence, the third option is correct.
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