Question 11 SSC-CGL 2018 June 4
[NOTE: only math questions solved]
Question: After giving two successive discounts each of x% on the marked price of an item, total discount is Rs. 259.20. If the face value of the object is Rs. 720, what will be the value of x?
- 25
- 24
- 18
- 20
Method 1
Discount is $\displaystyle \text{MP} \times \bigg[1 - (1 - x)^2\bigg]$
Hence, $\displaystyle 720 \times \bigg[1 - (1 - x)^2\bigg] = 259.20$
$\displaystyle \implies 1 - (1 - x)^2 = \frac{259.20}{720} = 0.36$
$\displaystyle \implies 1 - x = \sqrt{1 - 0.36} = \sqrt {0.64} = 0.8$
$\displaystyle \implies x = 0.2$ or 20% Ans.
Method 2
Effective rate after two successive discounts, by a shortcut formula is $\displaystyle x (2 - x)$
Hence $\displaystyle 720 \times x(2 - x) = 259.20$
$\displaystyle \implies x (2 - x) = \frac{259.20}{720} = 0.36$
By cycling the options, or even, by observation, $\displaystyle x = 20 \%$ Ans
Method 3
If nothing else works, try estimation.
The overall discount is $\displaystyle \frac{259.20}{720} = 0.36$ or 36%
Each of the discounts approximates to 18%. But the case is of two successive discounts, hence, therefore, the first discount has to be, in any case, greater than 18%. Reject 18%, and try the next nearer option, i.e., 20%.
First discount of 20% gives discount = 20% of 720 = Re. 144
The second discount has to be further 20% less than the first discount, i.e, = 144 - 20% of 144 = 144 - 28.8 = 115.2.
The total overall discount is 144 + 115.2 = 259.20 Rs, which confirms 20% as the answer!
This Blog Post/Article "Question 11 SSC CGL 2018 June 4 Shift 1" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2020-02-07. Published on: 2020-01-31