Question : Directions: Which of the following interchange of numbers and mathematical signs would make the given equation correct?
28 + 7 × 10 ÷ 5 − 20 = 5
Option 1: 10 and 20; × and +
Option 2: 5 and 20; − and ÷
Option 3: 7 and 28; × and ÷
Option 4: 5 and 10; + and ÷
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Correct Answer: 5 and 10; + and ÷
Solution :
Given:
28 + 7 × 10 ÷ 5 − 20 = 5
Interchanging of numbers and mathematical signs given in the options,
First option:
10 and 20; × and +
28 + 7 × 10 ÷ 5 − 20 = 5
⇒ 28 × 7 + 20 ÷ 5 − 10 = 5
⇒ 28 × 7 + 4 − 10 = 5
⇒ 196 + 4 − 10 = 5
⇒ 200 − 10 = 190 ≠ 5
⇒ L.H.S ≠ R.H.S
Second option:
5 and 20; − and ÷
28 + 7 × 10 ÷ 5 − 20 = 20
⇒ 28 + 7 × 10 − 20 ÷ 5 = 20
⇒ 28 + 7 × 10 − 4 = 20
⇒ 28 + 70 − 4 = 20
⇒ 98 − 4 = 94 ≠ 20
⇒ L.H.S ≠ R.H.S
Third option:
7 and 28; × and ÷
28 + 7 × 10 ÷ 5 − 20 = 5
⇒ 7 + 28 ÷ 10 × 5 − 20 = 5
⇒ 7 + 2.8 × 5 − 20 = 5
⇒ 7 − 6 = 1 ≠ 5
⇒ L.H.S ≠ R.H.S
Fourth option:
5 and 10; + and ÷
28 + 7 × 10 ÷ 5 − 20 = 5
⇒ 28 ÷ 7 × 5 + 10 − 20 = 10
⇒ 4 × 5 + 10 − 20 = 10
⇒ 20 + 10 − 20 = 10
⇒ 30 − 20 = 10 = R.H.S
So, the fourth option satisfies the equation. Hence, the fourth option is correct.
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