Plz help
1) By selling and umbrella for $336, a shopkeeper loses 4%. At what price must he sell it to gain 4%?
2) Luxmi sold to sarees for $1980 each. On one, she lost 10% while on the other she gained 10% find her gain or loss percent in the whole transaction.
Answers & Comments
Answer:
to gain 4% on Umbrella new Selling Price will be Rs.364.
Step-by-step explanation:
Let x be the CP of an umbrella
SP
=Rs.350
So, CP of an umbrella is Rs.350.
New SP to gain 4%
SP
= Rs.364
Verified answer
Answer:
[tex]\qquad \:\boxed{\begin{aligned}& \qquad \:\sf \:(1) \: \: Selling \: Price \: of \: umbrella = \$ \: 364\qquad \: \\ \\& \qquad \:\sf \:(2) \: \: Loss \: \% \: = \: 1 \end{aligned}} \qquad \: \\ \\ [/tex]
Step-by-step explanation:
[tex]\large\underline{\sf{Solution-1}}[/tex]
Given that,
Selling Price of an umbrella = $ 336
Loss % = 4
We know,
Selling Price, Cost Price and Loss % are connected by the relationship
[tex]\sf \: Cost \: Price \: = \: \dfrac{100 \times Selling \: Price}{100 - Loss\%} \\ \\ [/tex]
On substituting the values, we get
[tex]\sf \: Cost \: Price \: = \: \dfrac{100 \times 336}{100 - 4} \\ \\ [/tex]
[tex]\sf \: Cost \: Price \: = \: \dfrac{100 \times 336}{96} \\ \\ [/tex]
[tex]\sf \: Cost \: Price \: = \: \dfrac{100 \times 21}{6} \\ \\ [/tex]
[tex]\sf \: Cost \: Price \: = \: \dfrac{100 \times 7}{2} \\ \\ [/tex]
[tex]\sf\implies \sf \: Cost \: Price \: = \: \$ \: 350 \\ \\ [/tex]
Now,
Cost Price of an umbrella = $ 350
Gain % = 4
We know,
Selling Price, Cost Price and Gain % are connected by the relationship
[tex]\sf \: Selling \: Price \: = \: \dfrac{(100 + Gain\%) \times Cost \: Price}{100} \\ \\ [/tex]
So, on substituting the values, we get
[tex]\sf \: Selling \: Price \: = \: \dfrac{(100 + 4) \times 350}{100} \\ \\ [/tex]
[tex]\sf \: Selling \: Price \: = \: \dfrac{104 \times 35}{10} \\ \\ [/tex]
[tex]\sf \: Selling \: Price \: = \: \dfrac{104 \times 7}{2} \\ \\ [/tex]
[tex]\sf\implies \sf \: Selling \: Price \: = \: \$ \: 364 \\ \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
[tex]\large\underline{\sf{Solution-2}}[/tex]
Case :- 1
Selling Price of a saree = $ 1980
Loss % = 10
We know,
Selling Price, Cost Price and Loss % are connected by the relationship
[tex]\sf \: Cost \: Price \: = \: \dfrac{100 \times Selling \: Price}{100 - Loss\%} \\ \\ [/tex]
[tex]\sf \: Cost \: Price \: = \: \dfrac{100 \times 1980}{100 - 10} \\ \\ [/tex]
[tex]\sf \: Cost \: Price \: = \: \dfrac{100 \times 1980}{90} \\ \\ [/tex]
[tex]\sf \: Cost \: Price \: = \: 100 \times 20 \\ \\ [/tex]
[tex]\sf\implies \sf \: Cost \: Price \: = \: \$ \: 2200 \\ \\ [/tex]
Case :- 2
Selling Price of a saree = $ 1980
Gain % = 10
We know,
Selling Price, Cost Price and Gain % are connected by the relationship
[tex]\sf \: Cost \: Price \: = \: \dfrac{100 \times Selling \: Price}{100 + Gain\%} \\ \\ [/tex]
[tex]\sf \: Cost \: Price \: = \: \dfrac{100 \times 1980}{100 + 10} \\ \\ [/tex]
[tex]\sf \: Cost \: Price \: = \: \dfrac{100 \times 1980}{110} \\ \\ [/tex]
[tex]\sf \: Cost \: Price \: = \:100 \times 18 \\ \\ [/tex]
[tex]\sf\implies \sf \: Cost \: Price \: = \: \$ \: 1800 \\ \\ [/tex]
So, from above two cases, we concluded that,
[tex]\sf \: Cost \: Price \: of \: sarees = 2200 + 1800 = \$ \: 4000 \\ \\ [/tex]
and
[tex]\sf \: Selling \: Price \: of \: sarees = 1980 + 1980 = \$ \: 3960 \\ \\ [/tex]
Thus,
[tex]\sf\implies \sf \: Cost \: Price \: > \: Selling \: Price \\ \\ [/tex]
[tex]\sf\implies \sf \: Loss \: in \: this \: transaction. \\ \\ [/tex]
So,
[tex]\sf \: Loss\% = \dfrac{Cost \: Price - Selling \: Price}{Cost \: Price} \times 100 \\ \\ [/tex]
[tex]\sf \: Loss\% = \dfrac{4000 - 3960}{4000} \times 100 \\ \\ [/tex]
[tex]\sf \: Loss\% = \dfrac{40}{40} \\ \\ [/tex]
[tex]\sf\implies \sf \: Loss\% = 1 \\ \\ [/tex]