Question : Directions: Which two signs and two numbers should be interchanged in the following equation to make it correct?
20 – 10 × 342 ÷ 19 + 51 = 211
Option 1: 51 and 20, – and +
Option 2: 20 and 342, – and ÷
Option 3: 10 and 20, – and ×
Option 4: 19 and 342, × and ÷
Correct Answer: 51 and 20, – and +
Solution :
Given:
20 – 10 × 342 ÷ 19 + 51 = 211
Interchange the numbers and signs in the options one by one in the given equation.
First option:
51 and 20, – and +
20 – 10 × 342 ÷ 19 + 51 = 211
⇒ 51 + 10 × 342 ÷ 19 – 20 = 211
= 51 + 10 × 18 – 20
= 51 + 180 – 20
= 211 = R.H.S.
Second option:
20 and 342, – and ÷
20 – 10 × 342 ÷ 19 + 51 = 211
⇒ 342 ÷ 10 × 20 – 19 + 51 = 211
= 34.2 × 20 –19 + 51
= 684 – 19 + 51
= 716 ≠ 211
Third option:
10 and 20, – and ×
20 – 10 × 342 ÷ 19 + 51 = 211
⇒10 × 20 – 342 ÷ 19 + 51 = 211
= 10 × 20 – 18 + 51
= 200 – 18 + 51
= 233 ≠ 211
Fourth option:
19 and 342, × and ÷
20 – 10 × 342 ÷ 19 + 51 = 211
⇒ 20 – 10 ÷ 19 × 342 + 51 = 211
= 20 – 0.53 × 342 + 51
= 20 – 181.26 + 51
= –110.26 ≠ 211
So, only the first option satisfies the R.H.S. of the given equation, when the numbers are changed. Hence, the first option is correct.
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