Question : Directions: Which two signs and two numbers should be interchanged to make the following equation correct?
784 ÷ 6 × 9 – 30 + 14 = 528

Option 1: 14 and 6, + and –

Option 2: 784 and 30, + and x

Option 3: 784 and 6, × and –

Option 4: 9 and 6, + and ÷

Correct Answer: 14 and 6, + and –

Solution : Given:
784 ÷ 6 × 9 – 30 + 14 = 528

Let's check the options –
First option: 14 and 6, + and –
On interchanging the numbers and signs, the equation becomes –
784 ÷ 14 × 9 + 30 – 6 = 528
Solving the L.H.S. of the equation –
= 56 × 9 + 30 – 6
= 504 + 30 – 6
= 534 – 6
= 528
Second option: 784 and 30, + and ×
On interchanging the numbers and signs, the equation becomes –
30 ÷ 6 + 9 – 784 × 14 = 528
Solving the L.H.S. of the equation –
= 5 + 9 – 784 × 14
= 5 + 9 – 10976
= 14 – 10976
= –10962 ≠ 528
Third option: 784 and 6, × and –
On interchanging the numbers and signs, the equation becomes –
6 ÷ 784 – 9 × 30 + 14 = 528
Solving the L.H.S. of the equation –
= 0.0077 – 9 × 30 + 14
= 0.0077 – 270 + 14
= 14.0077 – 270
= –255.99 ≠ 528
Fourth option: 9 and 6, + and ÷
On interchanging the numbers and signs, the equation becomes –
784 + 9 × 6 – 30 ÷ 14 = 528
Solving the L.H.S. of the equation –
= 784 + 9 × 6 – 2.14
= 784 + 54 – 2.14
= 838 – 2.14
= 835.86 ≠ 528

So, from the above, only the first option satisfies the given equation. Hence, the first option is correct.