Question : Directions: Which of the following interchanges of numbers and mathematical signs would make the given equation correct?
729 × 81 ÷ 20 + 16 − 6 = 50
Option 1: 6 and 20, × and ÷
Option 2: 20 and 50, + and −
Option 3: 16 and 50, × and +
Option 4: 16 and 20, + and ÷
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Correct Answer: 6 and 20, × and ÷
Solution :
Given:
729 × 81 ÷ 20 + 16 − 6 = 50
Let's check the given options –
First option:
6 and 20, × and ÷
On interchanging the signs and numbers, we get –
⇒ 729 ÷ 81 × 6 + 16 − 20 = 50
Solving the L.H.S. of the equation –
= 9 × 6 + 16 − 20
= 54 + 16 − 20
= 70 − 20
= 50
Second option:
20 and 50, + and −
On interchanging the signs and numbers, we get –
⇒ 729 × 81 ÷ 50 − 16 + 6 = 20
Solving the L.H.S. of the equation –
= 729 × 1.62 − 16 + 6
= 1180.98 − 16 + 6
= 1186.98 – 16
= 1170.98 ≠ 20
Third option:
16 and 50, × and +
On interchanging the signs and numbers, we get –
⇒ 729 + 81 ÷ 20 × 50 − 6 = 16
Solving the L.H.S. of the equation –
= 729 + 4.05 × 50 − 6
= 729 + 202.50 – 6
= 931.50 – 6
= 925.5 ≠ 16
Fourth option:
16 and 20, + and ÷
On interchanging the signs and numbers, we get –
⇒ 729 × 81 + 16 ÷ 20 − 6 = 50
Solving the L.H.S. of the equation –
= 729 × 81 + 0.80 − 6
= 59049 + 0.80 – 6
= 59049.80 – 6
= 59043.80 ≠ 50
So, only the first option satisfies the given equation. Hence, the first option is correct.
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