# (solved)Question 11 SSC-CGL 2018 June 4 Shift 1

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?
(Rev. 03-Aug-2022)

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### Question 11SSC-CGL 2018 June 4 Shift 1

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

### Solution in Brief

Starting price = Rs. 720. There are two successive disounts compounded at $\displaystyle x\%$. Final price by compound formula is $\displaystyle 720(1 - x)^2$

Hence the total discount is $\displaystyle 720(1 - x)^2 - 720$ = $\displaystyle 720x(x - 2)$, which can be equated to the given figure of 259.20 to get: 720x(2 - x) = 259.29

Next, we can cycle through the options to obtain x = 0.2 or 20% as the answer!

### Solution in Detail

Starting Marked Price = $\displaystyle 720$ Rs.

First $\displaystyle \%$ discount is $\displaystyle x$

$\displaystyle \therefore$ first discount = Rs. $\displaystyle 720 \times x \text{ . . . (1)}$

$\displaystyle \therefore$ Price = $\displaystyle 720 - 720x = 720(1 - x)$

Second discount is again of $\displaystyle x\%$

$\displaystyle \therefore = [720(1 - x)] x\text{. . . (2)}$

Total discount = $\displaystyle (1) + (2)$

$\displaystyle = 720 x + 720(1 - x) x$

$\displaystyle = 720 x [1 + (1 - x)]$

$\displaystyle = 720 x \times (2 - x)$

It has been given as 259.20

$\displaystyle \implies 720 x \times (2 - x) = 259.20$

Cycling through the options, x = 0.2 or 20% is the answer!

### Solution by Alternate Method

This is a standard shortcut formula that can be memorized

Effective rate after two successive and same discounts 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

### Solution by Another Alternate Method

Discount is $\displaystyle \text{MP} \times [1 - (1 - x)^2]$

EXPLANATION: sale price after first discount is $\text{MP} - (\text{MP} \times x)$ = $\text{MP}(1 - x)$. This becomes marked price for the second discount, giving the final sale price of $[\text{MP}(1 - x)] \times (1 - x) = \text{MP}(1 - x)^2$, whence the above expression.

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.

### Solution by 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!