Question

If the values of a=3567, b=10, c=100, d=1000& e=10000. What are the options that the value of $ \dfrac{a}{b}+\dfrac{a}{c}-\dfrac{a}{d}+\dfrac{a}{e} $ is less than their value?
(a) 3.962937
(b) 3962.937
(c) 39.62937
(d) 39629.37

Answer 1

Hint: We have values of a, b, c, d, e given in the problem. We find values of $ \dfrac{a}{b} $ , $ \dfrac{a}{c} $ , $ \dfrac{a}{d} $ and $ \dfrac{a}{e} $ individually. After calculating the values individually, we make additions and subtractions individually to get the required value. Once we get the value, we check in the options which are greater than the obtained value.

Complete step-by-step answer:
We have the values of a=3567, b=10, c=100, d=1000& e=10000 given respectively. We need to find the value of $ \dfrac{a}{b}+\dfrac{a}{c}-\dfrac{a}{d}+\dfrac{a}{e} $ . Let us assume the value be ‘x’. We also need to check which options have the greater value than ‘x’.
So, $ x=\dfrac{a}{b}+\dfrac{a}{c}-\dfrac{a}{d}+\dfrac{a}{e} $ ---(1).
Let us first find the value of $ \dfrac{a}{b} $ .
 $ \dfrac{a}{b}=\dfrac{3567}{10} $ .
 $ \dfrac{a}{b}=356.7 $ ---(2).
Now, let us find the value of $ \dfrac{a}{c} $ .
 $ \dfrac{a}{c}=\dfrac{3567}{100} $ .
 $ \dfrac{a}{c}=35.67 $ ---(3).
Now, let us find the value of $ \dfrac{a}{d} $ .
 $ \dfrac{a}{d}=\dfrac{3567}{1000} $ .
 $ \dfrac{a}{d}=3.567 $ ---(4).
Now, let us find the value of $ \dfrac{a}{d} $ .
 $ \dfrac{a}{d}=\dfrac{3567}{1000} $ .
 $ \dfrac{a}{d}=3.567 $ ---(5).
Now, let us find the value of $ \dfrac{a}{e} $ .
 $ \dfrac{a}{e}=\dfrac{3567}{10000} $ .
 $ \dfrac{a}{e}=0.3567 $ ---(6).
Now, we substitute results obtained from equations (2), (3), (4), (5) & (6) in equation (1) to get the value of ‘x’.
 $ x=\dfrac{a}{b}+\dfrac{a}{c}-\dfrac{a}{d}+\dfrac{a}{e} $ .
x = 356.7+35.67-3.567+0.3567.
x=389.1597.
∴ The value of $ \dfrac{a}{b}+\dfrac{a}{c}-\dfrac{a}{d}+\dfrac{a}{e} $ is 389.1597.
We can see from the options 389.1597 is less than 3962.937 and 39629.37.
So, the correct answer is “Option B and D”.

Note: Here we need to do subtraction and addition without making any calculation mistakes. Since this problem has a multiple answer, we got two options. It is preferable to calculate each term separate and add/subtract at last to avoid confusion and calculation mistakes.