Question : Directions: Which of the following interchanges of signs and numbers would make the given equation correct?
25 – 10 ÷ 5 + 15 × 30 = 55
Option 1: × and ÷, 30 and 25
Option 2: ÷ and +, 15 and 10
Option 3: × and –, 15 and 10
Option 4: + and –, 5 and 10
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Correct Answer: × and –, 15 and 10
Solution :
Given:
25 – 10 ÷ 5 + 15 × 30 = 55
Let's check the options –
First option
: × and ÷, 30 and 25
⇒ 30 – 10 × 5 + 15 ÷ 25 = 55
Solving the L.H.S. of the equation –
= 30 – 10 × 5 + 0.6
= 30 – 50 + 0.6
= 30.6 – 50
= –19.4
≠
55
Second option:
÷ and +, 15 and 10
⇒ 25 – 15 + 5 ÷ 10 × 30 = 55
Solving the L.H.S. of the equation –
= 25 – 15 + 0.5 × 30
= 25 – 15 + 15
= 40 – 15
= 25
≠
55
Third option:
× and –, 15 and 10
⇒ 25 × 15 ÷ 5 + 10 – 30 = 55
Solving the L.H.S. of the equation –
= 25 × 3 + 10 – 30
= 75 + 10 – 30
= 85 – 30
= 55 = R.H.S.
Fourth option:
+ and –, 5 and 10
⇒ 25 + 5 ÷ 10 – 15 × 30 = 55
Solving the L.H.S. of the equation –
= 25 + 0.5 – 15 × 30
= 25 + 0.5 – 450
= 25.5 – 450
= –424.5
≠
55
So, only the third option satisfies the given equation. Hence, the third option is correct.
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