Percentage - Study Mode

[#226] A monthly return railway ticket cost 25 percent more than a single ticket. A week's extension can be had for the former by paying 5 percent of the monthly ticket's cost. If the money paid for the monthly ticket (with extension) is Rs. 84, the price of the single ticket is :
Correct Answer

(B) Rs. 64

Explanation

Solution: Let the cost of a single ticket be Rs. $$x$$ The, cost of monthly return ticket : $$eqalign{
& = 125\% ,,{ ext{of}},,{ ext{Rs}}.x cr
& = { ext{Rs}}{ ext{. }}left( {frac{{125}}{{100}}x}
ight) cr
& = { ext{Rs}}{ ext{. }}frac{{5x}}{4} cr} $$ Cost of monthly return ticket with extension : $$eqalign{
& = 105\% ,,{ ext{of}},,{ ext{Rs}}.frac{{5x}}{4} cr
& = { ext{Rs}}{ ext{. }}left( {frac{{105}}{{100}} imes frac{{5x}}{4}}
ight) cr
& = { ext{Rs}}{ ext{. }}frac{{21x}}{{16}} cr} $$ $$eqalign{
& herefore frac{{21x}}{{16}} = 84 cr
& Rightarrow x = left( {frac{{84 imes 16}}{{21}}}
ight) cr
& Rightarrow x = 64 cr} $$

[#227] Fresh grapes contain 80 percent water while dry grapes contain 10 percent water. If the weight of dry grapes is 250 kg what was its total weight when it was fresh ?
Correct Answer

(C) 1125 kg

Explanation

Solution: Quantity of pulp in fresh grapes = Quantity of pulp in dry grapes = (100 - 10)% of 250 kg = 90% of 250 kg = 225 kg Let the total weight of fresh grapes be $$x$$ kg Then, ⇒ (100 - 80)% of $$x$$ = 225 ⇒ 20% of $$x$$ = 225 ⇒ $$frac{x}{5}$$ = 225 ⇒ $$x$$ = 225 × 5 ⇒ $$x$$ = 1125 Hence, total weight of fresh grapes = 1125 kg

[#228] When income tax is 3 paise in a rupee, a person's net income is Rs. 237650. What will it be when the income tax is raised to 7 paise ?
Correct Answer

(C) Rs. 227850

Explanation

Solution: Let the person's gross income be Rs. $$x$$ Then, ⇒ (100 - 3)% of $$x$$ = 237650 ⇒ 97% of $$x$$ = 237650 ⇒ $$frac{97x}{100}$$ = 237650 ⇒ $$x$$ = $$left( {frac{{237650 imes 100}}{{97}}}
ight)$$ ⇒ $$x$$ = 245000 ∴ When income tax is raised to 7%, we have : Net income : = (100 - 7)% of Rs. 245000 = 93% of Rs. 245000 = Rs. $$left( {frac{{93}}{{100}} imes 245000}
ight)$$ = Rs. 227850

[#229] In a certain month a base ball team that played 60 games had won 30% of its games played. After a phenomenal winning streak this team raised its average to 50%. How many games must the team have won in a row to attain this average ?
Correct Answer

(C) 24

Explanation

Solution: Number of games already won = 30% of 60 = 18 Let the required number of games be $$x$$ Then, $$eqalign{
& Rightarrow frac{{18 + x}}{{60 + x}} imes 100 = 50 cr
& Rightarrow frac{{18 + x}}{{60 + x}} = frac{1}{2} cr
& Rightarrow 36 + 2x = 60 + x cr
& Rightarrow x = 24 cr} $$

[#230] The numbers are respectively $$12frac{1}{2}\% $$xa0 and $$25\% $$ more than a third number. The as a percentage of the second number is :
Correct Answer

(D) 90%

Explanation

Solution: Let the third number be $$x$$ Then, first number : = $$112frac{1}{2}\% $$xa0 of $$x$$ = $$frac{9x}{8}$$ Second number : = 125% of $$x$$ = $$frac{5x}{4}$$ ∴ Required percentage : = $$left( {frac{{9x}}{8} imes frac{{4}}{{5x}} imes 100}
ight)$$ xa0 % = 90%