Question

1. Find the cost price, if :
(i) S.P. = 21 and gain = 5%
(ii) S.P. = * 340 and gain = 20
(v) S.P. = * 1 and loss = 5 p​

Answer 1

Answer:

1. Find the Cost Price, if :-

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(i) S.P. = 21 and gain = 5%

Solution -

$\red\implies \sf \purple{C.P} = \pink{S.P \times \dfrac{100}{100 +Profit \% }}$

So,

$\red \implies \sf \pink{C.P} = \purple{21 \times \dfrac{100}{100 + 5} }$

$\red\implies\sf \pink{C.P }= \purple{21\times \dfrac{100} {105} }$

$\red\implies \sf \pink{C.P }= \purple{ \cancel\dfrac{2100}{105} }$

$\red\implies \sf \pink{C.P} = \purple{20}$

Therefore

The Cost Price is ₹20.

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(ii) S.P. = * 340 and gain = 20

Solution

$\blue\longrightarrow\sf \purple{C.P} = \pink{S.P - Gain}$

So,

$\blue \longrightarrow\sf \pink{C.P }= \purple{ 340 - 20}$

$\blue \longrightarrow\sf \pink{C.P }= \purple{320}$

Therefore

The Cost Price is ₹320.

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(iii) S.P. = * 1 rupee and loss = 5 p

Solution -

$\orange\longmapsto\sf \purple{C.P} = \pink{S.P + loss}$

So,

Firstly we convert the paisa into ruree.

$\orange \longmapsto\sf \pink{Rupee} = \purple{\dfrac{Paise}{100} }$

$\orange\longmapsto \sf \pink{Rupee}= \purple{\dfrac{5}{100} }$

$\orange \longmapsto\sf \pink{Rupee} = \purple {0.05 }$

Now,

$\orange\longmapsto\sf \pink{C.P} = \purple{1 + 0.05}$

$\orange \longmapsto\sf \pink{C.P} = \purple{1.05}$

Therefore

The Cost Price is 1.05 rupee.

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 Some related formulae :-

$\sf \pink{Profit} :- \purple{\boxed{\tt SP-CP}}$

$\sf \pink{Loss}:- \purple{\boxed{\tt CP-SP}}$

$\sf { \pink{Profit \: percentage} :- \purple{\boxed{\tt\dfrac{Profit}{CP} \times 100}}}$

$\sf \pink{Loss \: percentage }:-\purple{\boxed{\tt\dfrac{Loss}{CP} \times 100}}$