Atul sold a television set and a mobile phone for 10,500, thereby making a profit of 10%
on the television set and 25% on the mobile phone. If he had taken a profit of 25% on the
television set and 10% on the mobile phone, he would have got 7 10,650. Find the cost price of each item
Answers
Answer:
Answer:-
Given:
Case - 1 :-
SP of telivision set and mobile phone = Rs. 10500
Let SP of telivision set be x.
So, SP of Mobile phone = 10500 - x
Also given that,
Profit% on telivision set = 10%
Profit% on mobile phone = 25%.
We know that,
CP = (100 / 100 + Profit% ) * SP
So,
CP of telivision set = (100 / 100 + 10 ) * x
⟶ CP of telivision set = 100x/110
⟶ CP of telivision set = Rs. 10x/11 -- (1)
Similarly,
CP of mobile phone = 100(10500 - x) / 100 + 25
⟶ CP of mobile phone = 100(10500 - x) / 125
⟶ CP of mobile phone = Rs. 4(10500 - x)/5 -- (2)
Case - 2 :
Profit % on telivision set = 25%
Profit% on mobile phone = 10%
Total SP of items = 10650
\sf \longrightarrow \dfrac{10x}{11} \times \dfrac{100 + 25}{100} + \dfrac{4(10500 - x)}{5} \times \dfrac{100 + 10}{100} = 10650⟶
11
10x
×
100
100+25
+
5
4(10500−x)
×
100
100+10
=10650
[ From equations (1) & (2) ]
\begin{gathered} \longrightarrow \sf \: \: \frac{10x(125)}{1100} + \frac{110(42000 - 4x)}{500} = 10650 \\ \\ \\ \longrightarrow \sf \: \frac{5 \times 1250x + 11 \times 110 \times (42000 - 4x)}{5500} = 10650 \\ \\ \\ \longrightarrow \sf \: 6250x + 50820000 - 4840x = 10650 \times 5500 \\ \\ \\ \longrightarrow \sf \:1410x = 58575000 - 50820000 \\ \\ \longrightarrow \sf \: 1410x = 7755000 \\ \\ \longrightarrow \sf \:x = \frac{7755000}{1410} \\ \\ \longrightarrow \boxed{\sf \:x = 5500}\end{gathered}
⟶
1100
10x(125)
+
500
110(42000−4x)
=10650
⟶
5500
5×1250x+11×110×(42000−4x)
=10650
⟶6250x+50820000−4840x=10650×5500
⟶1410x=58575000−50820000
⟶1410x=7755000
⟶x=
1410
7755000
⟶
x=5500
Substitute the value of x in equation (1).
⟶ CP of telivision set = 10(5500)/11
⟶ CP of telivision set = Rs. 5000
Substitute the value of x in equation (2).
⟶ CP of mobile phone = 4(10500 - 5500)/5
⟶ CP of mobile phone = 4 (5000)/5
⟶ CP of mobile phone = Rs. 4000
∴
CP of telivision set is Rs. 5000
CP of mobile phone is Rs. 4000
Step-by-step explanation: