Question

A shopkeeper sold two watches for Rs. 920 each. On one watch he
gained 15% and on the other he lost 60%. Find his profit or loss percent.​

Answer 1

✬ Loss % = 40.64 % ✬

Step-by-step explanation:

Given:

• Selling price of two watches is Rs 920 each.
• On first watch he gained 15%.
• On second watch he lost 60%.

To Find:

• What is his overall profit or loss percent ?

Solution: We have to find the cost price of both watches.

To find C.P when S.P and profit/loss percent are given, we use following formula

When there is profit ➘

★ C.P = 100/ (100 + Profit %) × S.P ★

When there is loss ➘

★ C.P = 100/ (100 – Loss % ) × S.P ★

[ C.P of first watch ]

➟ 100/(100 + 15) × 920

➟ 100/115 × 920

➟ 92000/115

➟ 800

So C.P of first watch is Rs 800.

[ C.P of second watch ]

➟ 100/(100 – 60) × 920

➟ 100/40 × 920

➟ 92000/40

➟ 2300

So C.P of second watch is Rs 2300.

∴ Total S.P = 920 + 920 = Rs 1840

∴ Total C.P = 800 + 2300 = Rs 3100

• On comparison we got that C.P > S.P. It means he suffered a loss.

• Loss = C.P – S.P

• Loss = 3100 – 1840 = Rs 1260

∴ Loss % = Loss / C.P × 100

$\implies{\rm }$ Loss % = 1260/3100 × 100

$\implies{\rm }$ Loss % = 126000/3100

$\implies{\rm }$ Loss % = 40.64

Hence , he suffers a loss of 40.64 % on whole transaction.

Answer 2

${\boxed{\underline{\tt{ \orange{Required \: \: Answer:-}}}}}$

★GIVEN:-

• A shopkeeper sold two eatches at Rs. 920.

• At one watch profit % is 15%

• At another watch loss % is 60%

★TO FIND :-

• his profit or loss percent.

★SOLUTION:-

1st CASE:-

$: \implies \: \tt{S.P.\: = \:Rs. \:920}$

$: \implies\tt{Profit\% = 15\%}$

$: \implies \: \tt{C.P. = \frac{s.p. \times 100}{100 + p\%}}$

$: \implies \: \tt{C.P.\: =\: \frac{920×100}{100+15}}$

$: \implies \: \tt{C.P. \: =\: \frac{92000}{115}}$

$: \implies \: \tt{C.P.\:=\: Rs.800}$

2nd CASE:-

$: \implies \: \tt{S.P.\:=\:Rs.\:920}$

$: \implies \: \tt{Loss\% = 60\%}$

$: \implies \: \tt{C.P. = \frac{s.p. \times 100}{100 - loss\%}}$

$: \implies \: \tt{C.P. \: = \: \frac{920×100}{100-60}}$

$: \implies \: \tt{C.P. \: = \: \frac{92000}{40}}$

$: \implies \: \tt{C.P. \: = \: \frac{1200}{4}}$

$: \implies \: \tt{C.P.\:=\: Rs.300}$

_______________________________________________★

TOTAL C.P. = 2300 + 800

$: \implies \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\boxed{\underline{\tt{TOTAL \: \: C.P. = Rs.\:\:3100}}}}$

TOTAL S.P. = 920 + 920

$: \implies \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\boxed{\underline{\tt{TOTAL \: \: S.P. = Rs.\:\:1840}}}}$

SO,

S.P. < C.P.

Loss = 3100 - 1840

$: \implies \: {\boxed{\underline{\tt{loss = Rs.\:\:1260}}}}$

$: \implies \: \tt{Loss\% = \frac{loss}{C.P} \times 100}$

$: \implies \: \tt{Loss\% = \frac{1260}{3100} \times 100}$

$: \implies \: \tt{Loss\% = \frac{12600}{31}}$

$: \implies \: {\boxed{\underline{\tt{loss\% = 40.64\%}}}}$