Question

On selling a mobile for rupees 1600 a person
looses 20% then the cost price is
A. 32,400
B. $2,200
C. 2,000
D. 31,800​

Answer 1

Given:

• SP = Rs 1600

• Loss % = 20%

To calculate:

• CP = ?

Calculation:

As we know that,

$\sf{ C.P =\dfrac{100}{100-loss\%} \times S.P}$

$\sf { \implies C.P =\dfrac{100}{100-20} \times 1600}$

$\sf { \implies C.P =\dfrac{100}{80} \times 1600}$

$\sf { \implies C.P = 100 \times 20}$

$\implies$ $\boxed {\sf \red{ C.P = Rs \: 2000}}$

Therefore, the cost price is Rs 2000 and Option C is correct.

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$\small\boxed{ \begin{array}{cc}\large\sf\dag \: {\underline{More \: Formulae}} \\ \\ \bigstar \: \sf{Gain = S.P – C.P} \\ \\ \bigstar \:\sf{Loss = C.P – S.P} \\ \\ \bigstar \: \sf{Gain \: \% = \Bigg( \dfrac{Gain}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{loss \: \% = \Bigg( \dfrac{loss}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{S.P = \dfrac{100+Gain\%}{100} \times C.P} \\ \\ \bigstar \: \sf{ C.P =\dfrac{100}{100+Gain\%} \times S.P} \\ \\\bigstar \: \sf{ S.P = \dfrac{100-loss\%}{100} \times C.P} \\ \\ \bigstar \: \sf{ C.P =\dfrac{100}{100-loss\%} \times S.P}\end{array} }$

Answer 2

Given :-

• SP = Rs 1,600
• Loss % = 20%

To Calculate :-

• CP = ?

Calculation :

★ As we know that,

${\sf{C.P \: = \frac{100}{100 - loss %} \times S.P}}$

→ ${\sf{C.P \: = \frac{100}{100 - loss% 20} \times 1600}}$

→ ${\sf{C.P \: = \frac{100}{80} \times 1600}}$

→ ${\sf{C.P \: = 100 \: \times \: 20}}$

➝ $\boxed{\sf\green{C.P = Rs~2,000}}$

Therefore, the cost price is Rs 2,000 and Option C is correct.

__________________________

$\boxed{\underline{\bf{†More~Fornula}}$

★ ${\sf{\: \: \: \: \: Gain \: = \: S.P \: + \: C.P}}$

★ ${\sf{\: \: \: \: \: Loss \: = \: C.P \: - \: S.P}}$

★ ${\sf{Gain % \: \times \: ( \frac{Gain}{C.P} \: \times \: 100)%}}$

★ ${\sf{Loss % \: \times \: ( \frac{Loss}{C.P} \: \times \: 100)%}}$

★ ${\sf{S.P \: = \: 100 + \frac{Gain%}{100} \times C.P}}$

★ ${\sf{C.P \: = \: \frac{100}{100 \: + \: Gain%} \times S.P}}$

★ ${\sf{S.P \: = \: \frac{100 \: - \: Loss%}{100} \times C.P}}$

★ ${\sf{C.P \: = \: \frac{100}{100 \: - \: Loss%} \times S.P}}$