Question : Directions: Which two numbers, from amongst the given options, should be interchanged to make the given equation correct?
18 + (12 x 6) + (63 ÷ 7) x 4 + (27) – 11 = 112
Option 1: 18 and 11
Option 2: 12 and 4
Option 3: 6 and 4
Option 4: 18 and 12
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Correct Answer: 6 and 4
Solution :
Given:
18 + (12 x 6) + (63 ÷ 7) x 4 + (27)
⅓
– 11 = 112
Interchange the numbers given in the options one by one with the original numbers in the given equation.
First option:
18 and 11
18 + (12 x 6) + (63 ÷ 7) x 4 + (27)
⅓
– 11 = 112
⇒ 11 + (12 x 6) + (63 ÷ 7) x 4 + (27)
⅓
– 18 = 112
= 11 + 72 + 9 x 4 + 3
– 18 = 112
= 11 + 72 + 36 + 3
– 18 = 112
= 122 – 18 = 104 ≠ 112
Second option:
12 and 4
18 + (12 x 6) + (63 ÷ 7) x 4 + (27)
⅓
– 11 = 112
⇒ 18 + (4 x 6) + (63 ÷ 7) x 12 + (27)
⅓
– 11 = 112
=18 + 24 + 9 x 12 + 3
– 11 = 112
=18 + 24 + 108 + 3
– 11 = 112
=153
– 11 = 142 ≠ 112
Third option:
6 and 4
18 + (12 x 6) + (63 ÷ 7) x 4 + (27)
⅓
– 11 = 112
⇒ 18 + (12 x 4) + (63 ÷ 7) x 6 + (27)
⅓
– 11 = 112
=18 + 48 + 9 x 6 + 3
– 11 = 112
=18 + 48 + 54 + 3
– 11 = 112
=123
– 11 = 112 = R.H.S
Fourth option:
18 and 12
18 + (12 x 6) + (63 ÷ 7) x 4 + (27)
⅓
– 11 = 112
⇒ 12 + (18 x 6) + (63 ÷ 7) x 4 + (27)
⅓
– 11 = 112
= 12 + 108 + 9 x 4 + 3
– 11 = 112
= 12 + 108 + 36 + 3
– 11 = 112
= 159
– 11 = 148 ≠ 112
So, only the third option satisfies the R.H.S. of the given equation. Hence, the third option is correct.
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