Question

We are asked to think of a number, add 8 to it, and then multiply the sum so formed by 5. If the product is 160, the number we thought is
(a) 18 (b) 32 (c) 24 (d) 28

Answer 1

Hint: Here, we need to think of a number which when added with 8, and multiplied by 5, results in 160. We will assume the number to be \[x\] and apply the operations as stated. We will then equate the expression obtained after performing the stated operation to the product given to form an equation. We need to solve this equation to get the value of \[x\], and thus, obtain the required number.

Complete step-by-step answer:
We will apply the stated operations on the number we thought to get an equation.
Let the number we thought be \[x\].
First, we need to add 8 to the number we thought.
Thus, we get the sum as \[x + 8\].
Next, we need to multiply the sum obtained by 5.
Thus, we get the product as \[5\left( {x + 8} \right)\].
Now, we know that the product should be equal to 160.
Thus, equating the expression of the product obtained to 160, we get
\[5\left( {x + 8} \right) = 160\]
This is the equation obtained.
Now, we will simplify this equation to get the value of \[x\].
Multiplying the terms in the equation, we get
\[ \Rightarrow 5x + 40 = 160\]
Subtracting 40 from both sides of the equation, we get
\[\begin{array}{c} \Rightarrow 5x + 40 - 40 = 160 - 40\\ \Rightarrow 5x = 120\end{array}\]
Dividing both sides by 5, we get the value of \[x\] as
\[\begin{array}{c} \Rightarrow \dfrac{{5x}}{5} = \dfrac{{120}}{5}\\ \Rightarrow x = 24\end{array}\]
Hence, we get \[x = 24\] i.e. the number we thought of is 24.
\[\therefore\] The correct option is option (c).

Note: We can also check the given options one by one, add 8 to them, and multiply the sum by 5.
Adding 8 to option (a) 18, we get \[18 + 8 = 26\].
Multiplying this sum by 5, we get \[26 \times 5 = 130\], which is not equal to 160.
Therefore, option (a) is incorrect.
Now we will perform the same operation on option (b).
Adding 8 to 32, we get \[32 + 8 = 40\].
Multiplying this sum by 5, we get \[40 \times 5 = 200\].
As the product is not equal to 160, therefore option (b) is incorrect.
Again we will perform the same operation on option (c).
Adding 8 to 24, we get \[24 + 8 = 32\].
Multiplying this sum by 5, we get \[32 \times 5 = 160\].
The product is equal to 160, so the correct option is option (c).
As we got the correct answer we need not check the last option. By this method of hit and trial method we will get our answer.