Question

Anju bought two mobiles for ₹40,000. He sold one of them at a profit of 10% and the other at a loss of 15%. If the selling price of each mobile is the same. Find the cost price of each mobile.​

Answer 1

Solution :

$\bf{\purple{\underline{\bf{Given\::}}}}$

Anju bought two mobiles for Rs.40000. He sold one of them at a profit of 10% and the other at a loss of 15%. If the selling price of each mobile is the same.

$\bf{\purple{\underline{\bf{To\:find\::}}}}$

The cost price of each mobile.

$\bf{\purple{\underline{\bf{Explanation\::}}}}$

Let the 1st Mobile of Cost price be Rs.R

Let the 2nd Mobile of Cost price be Rs.M

So;

$\leadsto\tt{R+M=40000}\\\\\leadsto\sf{M=40000-R.......................(1)}$

&

$\underline{\underline{\bf{Selling\:price\:(S.P.)\:of\:1st\:mobile\::}}}}}$

$\mapsto\sf{S.P.=\dfrac{100+profit\%}{100} \times C.P.}\\\\\\\mapsto\sf{S.P.=\dfrac{100+10}{100} \times R}\\\\\\\mapsto\sf{S.P.=\dfrac{11\cancel{0}}{10\cancel{0}} \times R}\\\\\\\mapsto\sf{S.P.=\dfrac{11R}{10} }$

$\underline{\underline{\bf{Selling\:price\:(S.P.)\:of\:2nd\:mobile\::}}}}}$

$\mapsto\sf{S.P.=\dfrac{100-loss\%}{100} \times C.P.}\\\\\\\mapsto\sf{S.P.=\dfrac{100-15}{100} \times M}\\\\\\\mapsto\sf{S.P.=\cancel{\dfrac{85}{100} }\times M}\\\\\\\mapsto\sf{S.P.=\dfrac{17}{20} \times M}\\\\\\\mapsto\sf{S.P.=\dfrac{17M}{20} }$

A/q

$\mapsto\tt{\dfrac{11R}{1\cancel{0}} =\dfrac{17M}{2\cancel{0}} }\\\\\\\mapsto\tt{2(11R)=17M}\\\\\\\mapsto\tt{22R=17M}\\\\\\\mapsto\tt{22R=17(40000-R)\:\:\:[from(1)]}\\\\\\\mapsto\tt{22R=680000-17R}\\\\\\\mapsto\tt{22R+17R=680000}\\\\\\\mapsto\tt{39R=680000}\\\\\\\mapsto\tt{R=\cancel{\dfrac{680000}{39} }}\\\\\\\mapsto\tt{\red{R=Rs.17435.89}}$

Putting the value of R in equation (1),we get;

$\mapsto\tt{M=Rs.(40000-17435.89)}\\\\\mapsto\tt{\red{M=Rs.22564.11}}$

Thus;

$\underbrace{\sf{The\:cost\:price\:of\:1st\:mobile=Rs.17435.89}}}}}\\\underbrace{\sf{The\:cost\:price\:of\:2nd\:mobile=Rs.22564.11}}}}}$

Answer 2

Answer:

$\implies$ The cast price of 1st mobile Rs. 17435.89

$\implies$The cast price of 2nd mobile = Rs. 22564.11.

$\large\underline\mathrm{Given:-}$

• Anju bought two mobiles for ₹40,000. He sold one of them at a profit of 10% and the other at a loss of 15%. If the selling price of each mobile is the same.

$\large\underline\mathrm{To \: find}$

• The cast price of each mobile.

$\large\underline\mathrm{Solution}$

• Let the 1st mobile of cast price Rs. R
• Let the 2nd mobile of cast price be Rs. M

So,

$\implies$ R + M = 40000

$\implies$ M = 40000 - R ..(1)

Selling price of 1st mobile;

$\implies$ S.P = (100 + profit%)/100 × C.P

$\implies$ S.P = (100 + 10)/100 × R

$\implies$ S.P = 110/100 × R

$\implies$ S.P = 11R/10

Selling price of 2nd mobile;

$\implies$ S.P = (100 - loss%)/100 × C.P

$\implies$ S.P = (100 - 15)/100 × M

$\implies$ S.P = 85/100 × M

$\implies$ S.P = 85M/100

$\implies$ S.P = 17M/20

Now,

$\implies$ 11R/10 = 17M/20

$\implies$ 2(11R) = 17M

$\implies$ 22R + 17(40000 - R)

$\implies$ 22R = 680000 - 17R

$\implies$ 22R + 17R = 680000

$\implies$ 39R = 680000

$\implies$ R = 680000/39

$\implies$ R = Rs. 17435.89

Putting the value of R in equation (1) we get,

$\implies$ M = Rs. ( 40000 - 17435.89)

$\implies$ M = Rs. 22564.11

Thus,

The cast price of 1st mobile Rs. 17435.89

The cast price of 2nd mobile = Rs. 22564.11.