If a * b = 2a - 3b + ab, then 3 * 5 + 5 * 3 is equal to?
A. 22
B. 24
C. 26
D. 28
Answer: Option A
Solution (By Examveda Team)
$$\eqalign{ & 3*5 + 5*3 \cr & \Rightarrow 3*5 = 2 \times 3 - 3 \times 5 + 3 \times 5 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 6 - 15 + 15 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 6 \cr & \Rightarrow 5*3 = 2 \times 5 - 3 \times 3 + 3 \times 5 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10 - 9 + 15 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 16 \cr & \therefore 3*5 + 5*3 \cr & \Rightarrow 6 + 16 = 22 \cr} $$This Question Belongs to Arithmetic Ability >> Algebra
To solve the problem, we first need to understand the operation defined by ( a * b = 2a + 3b + ab ). We are asked to find the value of ( 3 * 5 + 5 * 3 ).
Let's break it down step by step.
### Step 1: Compute ( 3 * 5 )
Using the definition of the operation:
[
3 * 5 = 2(3) + 3(5) + (3)(5)
]
Calculate each term:
[
2(3) = 6
3(5) = 15
(3)(5) = 15
]
Now, add them together:
[
3 * 5 = 6 + 15 + 15 = 36
]
### Step 2: Compute ( 5 * 3 )
Using the definition of the operation:
[
5 * 3 = 2(5) + 3(3) + (5)(3)
]
Calculate each term:
[
2(5) = 10
3(3) = 9
(5)(3) = 15
]
Now, add them together:
[
5 * 3 = 10 + 9 + 15 = 34
]
### Step 3: Add the Results
Now, add the results of ( 3 * 5 ) and ( 5 * 3 ):
[
3 * 5 + 5 * 3 = 36 + 34 = 70
]
However, none of the provided options (A) 22, (B) 24, (C) 26, (D) 28 match the result of 70. This suggests there might be a mistake in the problem statement or the provided options.
But let's double-check the calculations to ensure there's no error.
### Re-evaluating the Calculations
Recompute ( 3 * 5 ):
[
3 * 5 = 2(3) + 3(5) + (3)(5) = 6 + 15 + 15 = 36
]
Recompute ( 5 * 3 ):
[
5 * 3 = 2(5) + 3(3) + (5)(3) = 10 + 9 + 15 = 34
]
Adding them:
[
36 + 34 = 70
]
The calculations are correct, and the result is indeed 70.
Given that none of the provided options match 70, it's possible that there's a typo in the problem or the options. However, based on the given operation and calculations, the correct answer should be 70.
**Final Answer:** 70 (Note: This does not match any of the provided options.)
when we will find 3*5
here a=3, b=5,putting in equation given we will find value of 3*5
when we will find 5*3
here a=5, b=3, putting in equation given we will find value of 5*3
after that we will add them
what does mean by* in question