Question

Bina Chand bought two kettles for Rs 1,625. She sold one of them at 20% profit
and the other at 20% loss. If the selling price of both kettles are same, find the
cost price of each kettles. Also calculate her gain or loss percent in the total
transaction​

Answer 1

AnswEr :

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

Bina Chand bought two kettles for Rs.1625. She sold one of them at 20% profit and other at 20% loss. If the selling price of both kettles are same.

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

The cost price of each kettles and also her gains or loss percent in the total transaction.

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

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

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

So,

$\leadsto\tt{R+M=1625}\\\\\leadsto\tt{\purple{M=1625-R...................(1)}}$

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

$\mapsto\sf{S.P.=\dfrac{100+profit\%}{100} \times C.P.}\\\\\\\mapsto\sf{S.P.=\dfrac{100+20}{100} \times R}\\\\\\\mapsto\sf{S.P.=\dfrac{12\cancel{0}}{10\cancel{0}} \times R}\\\\\\\mapsto\sf{S.P.=\dfrac{12}{10} \times R}\\\\\\\mapsto\sf{\red{S.P.=\dfrac{12R}{10} }}$

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

$\mapsto\sf{S.P.=\dfrac{100-loss\%}{100} \times C.P.}\\\\\\\mapsto\sf{S.P.=\dfrac{100-20}{100} \times M}\\\\\\\mapsto\sf{S.P.=\dfrac{8\cancel{0}}{10\cancel{0}} \times M}\\\\\\\mapsto\sf{S.P.=\dfrac{8}{10} \times M}\\\\\\\mapsto\sf{\red{S.P.=\dfrac{8M}{10} }}$

$\bf{\underline{\underline{\tt{A.T.Q\::}}}}}}$

$\leadsto\tt{\dfrac{12R}{\cancel{100}} =\dfrac{8M}{\cancel{100}} }\\\\\\\leadsto\tt{12R=8M}\\\\\\\leadsto\tt{12R=8(1625-R)}\\\\\\\leadsto\tt{12R=13000-8R}\\\\\\\leadsto\tt{12R+8R=13000}\\\\\\\leadsto\tt{20R=13000}\\\\\\\leadsto\tt{R=\cancel{\dfrac{13000}{20} }}\\\\\\\leadsto\tt{\red{R=Rs.650}}$

Then;

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

$\leadsto\tt{M=1625 -R}\\\\\\\leadsto\tt{M=1625-650}\\\\\\\leadsto\tt{\red{M=Rs.975}}$

Thus;

$\underbrace{\sf{The\:cost\:price\:of\:1st\:Kettle\:is\:R=Rs.650.}}}}\\\underbrace{\sf{The\:cost\:price\:of\:2nd\:Kettle\:is\:M=Rs.975.}}}}$

____________________________________________

Selling price of 1st kettle :

$\leadsto\sf{\dfrac{12R}{10} }\\\\\\\leadsto\sf{\dfrac{12\times 65\cancel{0}}{\cancel{10}}\:\:\:\:\big[R=Rs.650\big]} }\\\\\\\leadsto\sf{Rs.(12\times 65)}\\\\\\\leadsto\sf{Rs.780}}$

Selling price of 2nd kettle :

$\leadsto\sf{\dfrac{8M}{10} }\\\\\\\leadsto\sf{\dfrac{8\times 975}{10}\:\:\:\:\big[M=Rs.975\big]} }\\\\\\\leadsto\sf{Rs.(8\times 97.5)}\\\\\\\leadsto\sf{Rs.780}}$

Total Selling price of both kettle = Rs.(780+780)= Rs.1560.

Now,

→ Loss = Cost price - Selling price

→ Loss = Rs.1625 - Rs.1560

→ Loss = Rs.65.

$\bf{\large{\boxed{\bf{\red{Total\:loss\:(\%)of\:transaction\:of\:the\:kettle\::}}}}}}$

$\mapsto\tt{Loss\%=\dfrac{Loss\times 100}{C.P.} }\\\\\\\mapsto\tt{Loss\%=\dfrac{65\times 100}{1625}} \\\\\\\mapsto\tt{Loss\%=\cancel{\dfrac{6500}{1625} }}\\\\\\\mapsto\tt{\red{Loss\%=4\%}}$

∴ The total loss percent in the transaction is 4% .

Answer 2

$</p><p>\huge {\tt{\purple{Hello!!! }}}$

$</p><p>\huge {\fbox{\fbox{\rightarrow {\mathfrak {\pink{Question \: - }}}}}}$

• Bina Chand bought two kettles for Rs 1,625. She sold one of them at 20% profit and the other at 20% loss.

• If the selling price of both kettles are same, find the cost price of each kettles.

• Also calculate her gain or loss percent in the total transaction.

$</p><p>\huge {\fbox{\fbox{\rightarrow {\mathfrak {\red{Solution \: - }}}}}}$

$</p><p>\tt{\purple{CP \: 1 \: = \:Rs \: 650 . }}$

$</p><p>\tt{\green{CP \: 2 \: = \:Rs \: 975. }}$

$</p><p>\tt{\underline {\underline {\orange {Step-By-Step-Explaination \:: }}}}$

Answer :

$</p><p>\bf{\purple{\underline{\underline{\bf{Given\::}}}}}$

• Bina Chand bought two kettles for Rs.1625. She sold one of them at 20% profit and other at 20% loss. If the selling price of both kettles are same.

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

• The cost price of each kettles and also her gains or loss percent in the total transaction.

$\bf{\green{\underline{\underline{\bf{Solution\::}}}}}$

Let the 1st kettles of Cost price be Rs. A.Let the 2nd kettles of Cost price be Rs. B.

So,

$</p><p>\tt{\purple{A+B=1625}}$

$\tt{\purple{B=1625-A...................(1)}}$

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

$\sf{\pink{S.P.=\dfrac{100+profit\%}{100} \times C.P.}}$

$\sf{\red{S.P.=\dfrac{100+20}{100} \times A}}$

$\sf{\green{S.P.=\dfrac{12\cancel{0}}{10\cancel{0}} \times A}}$

$\sf{\blue{S.P.=\dfrac{12}{10} \times A}}$

$\sf{\green{S.P.=\dfrac{12A}{10} }}$

$</p><p>\blue {\bf{\underline{\underline{\bf{Selling\:price\:(S.P.)\:of\:2nd\:kettle\::}}}}}}$

$\purple{\sf{S.P.=\dfrac{100-loss\%}{100} \times C.P.}}$

${\pink{\sf{S.P.=\dfrac{100-20}{100} \times B}}}$

$</p><p>\red{\sf{S.P.=\dfrac{8\cancel{0}}{10\cancel{0}} \times B}}$

$</p><p>\green{\sf{S.P.=\dfrac{8}{10} \times B}}$

$</p><p>\pink{\sf{\red{S.P.=\dfrac{8B}{10} }}}$

$</p><p>\huge{\therefore{ \: }} </p><p></p><p>\red{\tt{\dfrac{12R}{\cancel{100}} =\dfrac{8B}{\cancel{100}}} }$

$\blue{\tt{12A=8(1625-B)}}$

Thus

$</p><p>\huge{\fbox{\fbox{\rightarrow {\mathfrak{\red{The\:cost\:price\:of\:1st\:Kettle\:is\:R=Rs.650.}}}}}}$

$</p><p>\huge{\fbox{\fbox{\rightarrow {\mathfrak{\purple{The\:cost\:price\:of\:2nd\:Kettle\:is\:M=Rs.975.}}}}}}$

___________________

Selling price of 1st kettle :

$</p><p>\huge{\fbox{\fbox{\rightarrow {\mathfrak{\red{Rs.780}}}}}}$

Selling price of 2nd kettle :

$</p><p>\huge{\fbox{\fbox{\rightarrow {\mathfrak{\red{Rs . 975}}}}} }$

Total Selling price of both kettle

$\huge{\fbox{\fbox{\rightarrow {\mathfrak{\red</strong><strong>{</strong><strong>=</strong> Rs.(780+780)= Rs.1560.}}}}}}$

→ Loss = Cost price - Selling price

→ Loss = Rs.1625 - Rs.1560

→ Loss

$\huge{\fbox{\fbox{\rightarrow {\mathfrak{\blue{= Rs. \: 65. }}}}}}$

$</p><p>\purple{\bf{\large{\boxed{\boxed{\bf{Total\:loss\:(\%)of\:transaction\:of\:the\:kettle\::}}}}}}$

$</p><p>\pink{\tt{Loss\%=\dfrac{Loss\times 100}{C.P.} = 4 \% }}$