Question

36. 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 10,650. Find the cost price
of each item.
​

Answer 1

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

$\sf \longrightarrow \dfrac{10x}{11} \times \dfrac{100 + 25}{100} + \dfrac{4(10500 - x)}{5} \times \dfrac{100 + 10}{100} = 10650$

[ From equations (1) & (2) ]

$\longrightarrow \sf \: \: \frac{10x(125)}{1100} + \frac{110(42000 - 4x)}{500} = 10650 \\ \\ \\ \longrightarrow \sf \: \frac{5 \times 1250x + 11 \times 110 \times (42000 - 4x)}{5500} = 10650 \\ \\ \\ \longrightarrow \sf \: 6250x + 50820000 - 4840x = 10650 \times 5500 \\ \\ \\ \longrightarrow \sf \:1410x = 58575000 - 50820000 \\ \\ \longrightarrow \sf \: 1410x = 7755000 \\ \\ \longrightarrow \sf \:x = \frac{7755000}{1410} \\ \\ \longrightarrow \boxed{\sf \:x = 5500}$

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

Answer 2

$\red{ \huge{question}}$

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 10,650. Find the cost price

of each item.

$\blue{ \huge{answer}}$

$given \: that$

Case:1

Selling price of television set and mobile phone =₹10,500

Let the of television set be 'x'

Then, Sp of mobile phone =₹10,500-x

$given..$

Profit% of television set = 25%

Profit% of Mobile phone = 10%

$we \: know \: that..$

Cp⤵️⤵️

[

$\frac{100}{100 + profit} \times sp$

So,

Cost price of television set ⤵️⤵️⤵️

$\frac{100}{100 + 10} \times x$

$\frac{100x}{110}$

Cp of television set ⬇️⬇️⬇️⬇️⬇️

$\frac{10x}{11}.....1$

Similarly,

Cost price of mobile phone ⤵️⤵️⤵️

$\frac{100(10500 - x}{100 + 25}</u></em></strong></p><p><strong><em><u>[tex]\frac{100(10500 - x}{100 + 25}$

Cost price of mobile phone⬇️⬇️⬇️⬇️⬇️

$\frac{4(10500 - x}{5...(2)}$

Case:2

Profit% of television set = 25%

Profit% of Mobile phone = 10%

Total Sp of products = ₹10,650

{from the equation(1)&(2)}

●CP of television set = ₹5000

●Cp of mobile phone =₹4000