### Interchange of signs based

In this type of questions are provided with substitutes for various mathematical symbols or numerals followed by a question involving calculation of an expression.

Note: While solving mathmatical expression according to theBODMASrule.

### Solved Problems

**Q.1.If ÷ means ×, × means +, + means – and – means ÷, then find the value of 16 × 3 + 5 – 2 ÷ 4.**

(a) 9

(b) 10

(c) 19

(d) None of these

Sol-

Using the correct symbols,

we have

Given expression :

16 + 3 – 5 ÷ 2 × 4 = 16 + 3 –5/2 × 4

= 19 – 10 = 9

**Q.2.If + means ÷, ÷ means –, – means ×, × means +, then 12 + 6 ÷ 3 – 2 × 8 = ?**

(a) –2

(b) 2

(c) 4

(d) 8

Sol.

Using the correct symbols,

we have

Given expression

= 12 ÷ 6 – 3 × 2 + 8 = 2 – 6 + 8 =

10 – 6 = 4

**Q.3.If + means –, – means ×, ÷ means + and × means ÷, then 15 – 3 + 10 × 5 + 5 = ?**

(a) 5

(b) 22

(c) 38

(d) 52

Sol.

Using the correct symbols,

we have

Given expression

= 15 × 3 – 10 ÷ 5 – 5 = 45 – 2 – 5

= 45 – 7 = 38

### Interchange of signs and numbers based

each of the following questions, if the given interchanges are made in signs and numbers, which one of the four equations would be correct?

**Q.1.Given interchanges : Signs – and ÷ and numbers 4 and 8.**

(a) 6–8÷4 = –1

(b) 8–6÷4 = 1

(c) 4÷8–2 = 6

(d) 4–8÷6 = 2

Sol.

On interchanging – and ÷ and 4 and 8 in (c), we get the

equation as :

8–4÷2=6 or 8 – 2 = 6 or 6 = 6, which is true.

**Q.2.Given interchanges : Signs + and × and numbers 4 and 5.**

(a) 5×4+20=40

(b) 5×4+20=85

(c) 5×4+20=104

(d) 5×4+20=95

Sol.

On interchanging + and × and 4 and 5 in (c), we get the

equation as :

4+5×20=104

104 = 104, which is true.