Model 1: If '+' means 'multiplied by', 'x' means 'minus', '÷' means 'plus' and '-' means 'multiplied by', then find the value of the expression 500 x 8 - 4 + 14 ÷ 72 ?
Solution:
Given expression:
500 x 8 - 4 + 14 ÷ 72
Now, by assigning the proper signs in the given expression,
500 - 8 ÷ 4 x 14 + 72
⇒ 492 ÷ 4 x 14 + 72
⇒ 123 x 14 + 72
⇒ 1722 + 72
⇒ 1794
Therefore, 500 x 8 - 4 + 14 ÷ 72 = 500 - 8 ÷ 4 x 14 + 72 = 1794
Model 2: If the equation is 10 - 2 + 9 x 2 ÷ 4 = 19. Then which of the following symbols satisfy the equation after replacing '-' and '÷' with optional symbols given?
a) – and ÷
b) – and +
c) ÷ and -
d) × and ÷
Solution:
Given that
Equation is 10 - 2 + 9 x 2 ÷ 4 = 19
Consider the option(a) i.e. replace '-' with '÷' and '÷' with '-'
Take L.H.S side of given equation
10 - 2 + 9 x 2 ÷ 4
Now, after interchanging
10 ÷ 2 + 9 x 2 - 4
⇒ 5 + 9 x 2 - 4
⇒ 5 + 18 - 4
⇒ 19
L.H.S. = R.H.S.
Therefore, option(a) is the correct option.
Model 3: If P + Q > S + T and Q + S > P + T, then what satisfy the given equations?
Solution:
Given that,
P + Q > S + T ---- (i)
Q + S > P + T ---- (ii)
Add equations (i) and (ii)
Then,
P + Q + Q + S > S + T + P + T
P + 2Q + S > S + 2T + P
2Q > 2 T
Q > T
Therefore, Q > T satisfy the given equations.
Model 4: If 8 × 6 × 4 = 648 and 3 × 6 × 5 = 653, then what is 3 × 9 × 8 ?
Solution:
Given that
8 × 6 × 4 = 648 and 3 × 6 × 5 = 653
From given expressions it is clear that
First number in LHS side is last number for RHS side, similarly second is first and last one is in the middle.
Similarly,
3 × 9 × 8 = 983.
Model 5: If * means 'is greater than', @ means `is less then’, and $ means 'is equal to' and if a $ b and b @ c, then find the relation?
Solution:
Given that
* means 'is greater than'
@ means `is less then’
$ means 'is equal to'
Consider a $ b and b @ c
Replace the symbols with the meaning given against them.
Then, a $ b and b @ c would become a = b and b < c, then c > b or c > a
i.e., c * b, c * a