Question 11 SSC CGL 2018 June 4 Shift 1

Posted by Parveen(Hoven),
Aptitude Trainer and Software Developer

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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?

1. 25
2. 24
3. 18
4. 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!