Profit And Loss - Study Mode

[#351] A man buys a cycle for Rs. 1400 and sells it at a loss of 15% . What is the selling price of the cycle = ?
Correct Answer

(B) Rs. 1190

Explanation

Solution: According to the question 15% loss, $$eqalign{
& ,,,,{ ext{CP}},,,,,,,,{ ext{Loss}},,,,,,,,,{ ext{SP}} cr
& mathop { downarrow imes 14}limits_{1400}^{100} ,,,,,,,,15,,,,,,mathop { downarrow imes 14}limits_{1190 o { ext{Answer}}}^{85} cr} $$

[#352] An article is sold at a profit of 20% . If the cost price is increased by 10% and the sale price by Rs. 26, then the percentage of profit reduces by 5% . Determine the cost price = ?
Correct Answer

(B) Rs. 400

Explanation

Solution: $$eqalign{
& { ext{Let the C}}{ ext{.P}}{ ext{. be Rs}}{ ext{. }}x cr
& { ext{Profit}} = 20\% cr
& { ext{S}}{ ext{.P}}{ ext{.}} = { ext{Rs}}.left( {frac{{120}}{{100}} imes x}
ight) cr
& ,,,,,,,,,,, = { ext{Rs}}{ ext{.}}frac{{6x}}{5} cr
& { ext{New C}}{ ext{.P}}{ ext{.}} = { ext{Rs}}{ ext{.}}left( {frac{{110}}{{100}} imes x}
ight) cr
& ,,,,,,,,,,,,,,,,,,,,,,,,, = { ext{Rs}}{ ext{.}}frac{{11x}}{{10}} cr
& { ext{New S}}{ ext{.P}}{ ext{.}} = { ext{Rs}}.left( {frac{{6x}}{5} + 26}
ight) cr
& { ext{New profit}} cr
& = { ext{Rs}}.left[ {left( {frac{{6x}}{5} + 26}
ight) - frac{{11x}}{{10}}}
ight] cr
& = { ext{Rs}}.left( {frac{x}{{10}} + 26}
ight) cr
& herefore left( {frac{x}{{10}} + 26}
ight) imes frac{{10}}{{11x}} imes 100 = 15 cr
& Rightarrow 100left( {x + 260}
ight) = 165x cr
& Rightarrow 65x = 26000 cr
& Rightarrow x = 400 cr} $$

[#353] Shailja earns 15 percent on an investment but loses 10 percent on another investment. If the ratio of the two investments is 3 : 5, then the combined loss percent is -
Correct Answer

(A) $$frac{5}{8}$$

Explanation

Solution: Let the two investments be Rs. 3x and Rs. 5x respectively. Then, Total investment = Rs. (3x + 5x) = Rs. 8x Total output = Rs. (115% of 3x + 90% of 5x) = Rs. (3.45x + 4.5x) = Rs. 7.95x Loss = Rs. (8x - 7.95x) = Rs. 0.05x $$eqalign{
& herefore { ext{Loss percent}} cr
& = left( {frac{{0.05x}}{{8x}} imes 100}
ight)\% cr
& = frac{5}{8}\% cr} $$

[#354] On selling an article for Rs. 651, there is a loss of 7%. The cost price of that article is = ?
Correct Answer

(D) Rs. 700

Explanation

Solution: According to the question 7% loss $$eqalign{
& ,,,{ ext{CP}},,,,,,,,{ ext{Loss}},,,,,,,,,{ ext{SP}} cr
& mathop { downarrow imes 7}limits_{mathop {700}limits_{left( {{ ext{Answer }}}
ight)} }^{100} ,,,,,,,,,,,7,,,,,,,mathop {,,,,,,, downarrow imes 7}limits_{651}^{93} cr} $$

[#355] A reduction of 20% in the price of salt enabled a purchaser to obtain 4 kg, more for Rs. 100. The reduced price of salt per kg. is = ?
Correct Answer

(B) Rs. 5/kg.

Explanation

Solution: Let the original price of salt per kg. is Rs. x So, purchaser can buy $$frac{{100}}{x}$$ kg. Now, reduction price is 20% Salt per kg. $$ = x imes frac{{80}}{{100}} = { ext{Rs}}{ ext{.}},frac{{4x}}{5}$$ Now purchaser can buy $$eqalign{
& frac{{100}}{{frac{{4x}}{5}}} = frac{{125}}{x},{ ext{kg}} cr
& herefore frac{{125}}{x} - frac{{100}}{x} = 4,{ ext{kg}} cr
& Rightarrow frac{{25}}{x} = 4 cr
& Rightarrow x = { ext{Rs}}{ ext{.}},6.25 cr} $$ Hence the reduced price of salt per kg. $$eqalign{
& = { ext{Rs}}{ ext{.}},6.25 imes frac{{80}}{{100}} cr
& = { ext{Rs}}{ ext{.}},5/{ ext{kg.}} cr} $$ Alternate: $$eqalign{
& { ext{Trick}} = frac{a}{x} imes frac{{{ ext{reduction}}}}{{100}} cr
& ,,,,,,,,,,,,,,,, = frac{{100}}{4} imes frac{{20}}{{100}} cr
& ,,,,,,,,,,,,,,,, = { ext{Rs}}{ ext{.}},5/{ ext{kg.}} cr} $$