A man bought 2 bicycles for ₹1250. He sold 1 of them. So as to gain 6% and the other at the loss of 4%. On the whole, he neither gained nor lost. How much did each cycle cost ?
Answers
Let assume that
- Cost Price of first bicycle is ₹ x
So,
- Cost Price of second bicycle is ₹ (1250 - x)
Case :- 1
- Cost Price = ₹ x
- Gain % = 6 %
So, Selling Price of bicycle is evaluated by using formula
So, on substituting the values, we get
Case :- 2
- Cost Price = ₹ (1250 - x)
- Loss % = 4 %
So, Selling Price of bicycle is evaluated by using formula
So, on substituting the values, we get
Now, According to statement, in the whole transaction, he neither gained nor loss.
Hence,
Cost Price of first bicycle = ₹ 500
Cost Price of second bicycle = 1250 - 500 = ₹ 750
Additional Information :-
Step-by-step explanation:
\large\underline{\sf{Solution-}}
Solution−
Let assume that
Cost Price of first bicycle is ₹ x
So,
Cost Price of second bicycle is ₹ (1250 - x)
Case :- 1
Cost Price = ₹ x
Gain % = 6 %
So, Selling Price of bicycle is evaluated by using formula
\begin{gathered}\boxed{ \rm{ \:Selling \: Price \: = \: \frac{(100 + Gain\%) \times Cost \: Price}{100} \: }} \\ \end{gathered}
SellingPrice=
100
(100+Gain%)×CostPrice
So, on substituting the values, we get
\begin{gathered}\rm \: Selling \: Price_1 = \dfrac{(100 + 6) \times x}{100} \\ \end{gathered}
SellingPrice
1
=
100
(100+6)×x
\begin{gathered}\rm\implies \:\boxed{ \rm{ \:\rm \: Selling \: Price_1 = \dfrac{106x}{100} \: }} - - (1) \\ \end{gathered}
⟹
SellingPrice
1
=
100
106x
−−(1)
Case :- 2
Cost Price = ₹ (1250 - x)
Loss % = 4 %
So, Selling Price of bicycle is evaluated by using formula
\begin{gathered}\boxed{ \rm{ \:Selling \: Price \: = \: \frac{(100 - Loss\%) \times Cost \: Price}{100} \: }} \\ \end{gathered}
SellingPrice=
100
(100−Loss%)×CostPrice
So, on substituting the values, we get
\begin{gathered}\rm \: Selling \: Price_2 = \dfrac{(100 - 4) \times (1250 - x)}{100} \\ \end{gathered}
SellingPrice
2
=
100
(100−4)×(1250−x)
\begin{gathered}\rm\implies \:\boxed{ \rm{ \:\rm \: Selling \: Price_2 = \dfrac{96(1250 - x)}{100} \: }} - - (2) \\ \end{gathered}
⟹
SellingPrice
2
=
100
96(1250−x)
−−(2)
Now, According to statement, in the whole transaction, he neither gained nor loss.
\begin{gathered}\rm\implies \:Selling \: Price_1 + Selling \: Price_2 = 1250 \\ \end{gathered}
⟹SellingPrice
1
+SellingPrice
2
=1250
\rm \: \dfrac{106x}{100} + \dfrac{96(1250 - x)}{100} = 1250
100
106x
+
100
96(1250−x)
=1250
\begin{gathered}\rm \: 106x + 96(1250 - x) = 1250 \times 100 \\ \end{gathered}
106x+96(1250−x)=1250×100
\begin{gathered}\rm \: 106x + 96 \times 1250 - 96x = 1250 \times 100 \\ \end{gathered}
106x+96×1250−96x=1250×100
\begin{gathered}\rm \: 106x - 96x = 1250 \times 100 \times 1250 \times 96 \\ \end{gathered}
106x−96x=1250×100×1250×96
\begin{gathered}\rm \: 10x = 1250 \times (100 - 96) \\ \end{gathered}
10x=1250×(100−96)
\begin{gathered}\rm \: x = 125 \times 4 \\ \end{gathered}
x=125×4
\begin{gathered}\rm\implies \:x = 500 \\ \end{gathered}
⟹x=500
Hence,
Cost Price of first bicycle = ₹ 500
Cost Price of second bicycle = 1250 - 500 = ₹ 750
\rule{190pt}{2pt}
Additional Information :-
\begin{gathered}\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{Gain = \sf S.P. \: – \: C.P.} \\ \\ \bigstar \:\bf{Loss = \sf C.P. \: – \: S.P.} \\ \\ \bigstar \: \bf{Gain \: \% = \sf \Bigg( \dfrac{Gain}{C.P.} \times 100 \Bigg)\%} \\ \\ \bigstar \: \bf{Loss \: \% = \sf \Bigg( \dfrac{Loss}{C.P.} \times 100 \Bigg )\%} \\ \\ \\ \bigstar \: \bf{S.P. = \sf\dfrac{(100+Gain\%) or(100-Loss\%)}{100} \times C.P.} \\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}\end{gathered}
MoreFormulae
MoreFormulae
★Gain=S.P.–C.P.
★Loss=C.P.–S.P.
★Gain%=(
C.P.
Gain
×100)%
★Loss%=(
C.P.
Loss
×100)%
★S.P.=
100
(100+Gain%)or(100−Loss%)
×C.P.