which of the following pairs are co primes 9 and 12
Answers
Step-by-step explanation:
merchant allows 25% discount on the marked price of the cycles and still makes a profit of 20/% If he gains 360 over the sale of one cycle.
Let assume that Marked Price of cycle be x.
Discount % = 25 %
We know,
\begin{gathered}\boxed{ \rm{ \:Selling \: Price = \frac{(100 - Discount\%)\times Marked \: Price}{100} \: }} \\ \end{gathered}
SellingPrice=
100
(100−Discount%)×MarkedPrice
So, on substituting the values, we get
\rm \: Selling \: Price = \dfrac{(100 - 25) \times x}{100}SellingPrice=
100
(100−25)×x
\rm \: Selling \: Price = \dfrac{75 \times x}{100}SellingPrice=
100
75×x
\begin{gathered}\rm\implies \:Selling \: Price \: = \: \dfrac{3x}{4} \\ \end{gathered}
⟹SellingPrice=
4
3x
Now, It is further given that after allowing 25% discount on the marked price of the cycles, he still makes a profit of 20 %
So, we know
\boxed{ \rm{ \:Cost \: Price = \frac{100 \times Selling \: Price}{100 + Profit\%} \: }}
CostPrice=
100+Profit%
100×SellingPrice
So, on substituting the values, we get
\begin{gathered}\rm \: Cost \: Price \: = \: \dfrac{100}{100 + 20} \times \dfrac{3x}{4} \\ \end{gathered}
CostPrice=
100+20
100
×
4
3x
\begin{gathered}\rm \: Cost \: Price \: = \: \dfrac{25}{120} \times 3x \\ \end{gathered}
CostPrice=
120
25
×3x
\begin{gathered}\rm \: Cost \: Price \: = \: \dfrac{25}{40} \times x \\ \end{gathered}
CostPrice=
40
25
×x
\begin{gathered}\rm \: Cost \: Price \: = \: \dfrac{5x}{8} \\ \end{gathered}
CostPrice=
8
5x
Now, Further given that, Gain on one cycle is 360
\begin{gathered}\rm \: Selling \: Price - Cost \: Price = 360 \\ \end{gathered}
SellingPrice−CostPrice=360
\begin{gathered}\rm \: \dfrac{3x}{4} - \dfrac{5x}{8} = 360 \\ \end{gathered}
4
3x
−
8
5x
=360
\begin{gathered}\rm \: \dfrac{6x - 5x}{8} = 360 \\ \end{gathered}
8
6x−5x
=360
\begin{gathered}\rm \: \dfrac{x}{8} = 360 \\ \end{gathered}
8
x
=360
\begin{gathered}\rm\implies \:x = 2880 \\ \end{gathered}
⟹x=2880
So, Marked price of cycle is 2880.
\rule{190pt}{2pt}
Additional Information :-
Answer:
When you take 3 & 8 ,where no number can be devisible by common number. Remaining have common devisors as 9 & 12 have 3 as common devisor, 15 & 3 also have 3 as common devisor,so they are not co prime pairs. I hope it helps you.