Which two numbers should be interchanged to make the following equation correct?
$$72 \div 9 \times 8 + 6 - 5 = 100$$

Solution

Option (a) 9 and 6

$$72 \div 6 \times 8 + 9 - 5 = 100$$

$$\frac{72}{6}\times8+9-5=100$$

$$12\times8+9-5=100$$
$$96+9-5=100$$
100=100
The given equation is satisfied. So this is the correct answer.

Option (b) 9 and 8

$$72 \div 8 \times 9 + 6 - 5 = 100$$

$$\frac{72}{8}\times9+6-5=100$$

$$9\times9+6-5=100$$
$$81+1=100$$
$$82\ne100$$
The given equation is not satisfied. So this is not the correct answer.

Option (c) 6 and 8

$$72 \div 9 \times 6 + 8 - 5 = 100$$

$$\frac{72}{9}\times6+8-5=100$$
$$8\times6+8-5=100$$
$$48+8-5=100$$
$$51\ne\ 100$$
The given equation is not satisfied. So this is not the correct answer.

Option (d) 9 and 5

$$72 \div 5 \times 8 + 6 - 9 = 100$$

The given equation is not satisfied. Because it will give values in fractions. So this is not the correct answer.