Percentage - Study Mode

[#201] Three candidates P, Q and R participated in an election. P got 35% more votes than Q, and R got 15% more votes than Q. P over took R by 2,412 votes. If 90% voters voted and no invalid or illegal votes were cast, then what was the number of voters in the voting list?
Correct Answer

(A) 46,900

Explanation

Solution: $$35\% = frac{7}{{20}},,15\% = frac{3}{{20}}$$ $$eqalign{
& Rightarrow 90\% = 42210 cr
& Rightarrow 100\% = frac{{42210}}{{90}} imes 100 = 46900 cr} $$

[#202] In a manufacturing unit, it was noted that the price of raw material has increased by 25% and the labor cost has gone up from 30% of the cost of raw material to 38% of the cost of the raw material. What percentage of the consumption of raw material be reduced to keep the cost the same as that before the increase?
Correct Answer

(C) 24.6%

Explanation

Solution: Raw material → 25% increase

[#203] Ramesh spends 40% of his monthly salary on food, 18% on house rent, 12% on entertainment, and 5% on conveyance. But due to a family function, he has to borrow Rs. 16,000 from a money lender to meet the expenses of Rs. 20,000. His monthly salary is:
Correct Answer

(C) Rs. 16,000

Explanation

Solution: Let monthly salary = 100x Total expenditure = (40 + 18 + 12 + 5)x = 75x 25x = 20,000 - 16,000 x $$ = frac{{4000}}{{25}} = 160$$ Hence monthly salary = 100x = 100 × 160 = 16,000

[#204] The value of a motorcycle depreciates every year by 4%. What will be its value after 2 years, if its present value is Rs. 75,000?
Correct Answer

(C) Rs. 69,120

Explanation

Solution: $$4\% o frac{{ - 1}}{{25}}$$

[#205] The price of diesel is increased by 26%. A person wants to increase his expenditure by 15% only. By what percentage, correct to one decimal place, should he decrease his consumption?
Correct Answer

(C) 8.7%

Explanation

Solution: Given: Percentage increase in the price of diesel = 26% Percentage increase in total expenditure = 15% Concept used: P × C = E Where P is Price, C is Consumption and E is Expenditure Calculation: Let initial price be P 1 , consumption be C 1 , and expenditure be E 1 P 1 × C 1 = E 1 ⇒ $${{ ext{C}}_1} = frac{{{{ ext{E}}_1}}}{{{{ ext{P}}_1}}}$$ Let new price be P 2 , new quantity consumed be C 2 , and new expenditure be E 2 P 2 = P 1 + 26% of P 1 ⇒ P 2 = 1.26P 1 E 2 = E 1 + 15% of E 1 ⇒ E 2 = 1.15E 1 As, P 2 × C 2 = E 2 ⇒ 1.26P 1 × C 2 = 1.15E 1 ⇒ C 2 = $$frac{{{ ext{1}}{ ext{.15}}{{ ext{E}}_1}}}{{{ ext{1}}{ ext{.26}}{{ ext{P}}_1}}}$$ ⇒ C 2 = 0.9126 × $$frac{{{{ ext{E}}_1}}}{{{{ ext{P}}_1}}}$$ ⇒ C 2 = 0.9126C 1 Decrease in consumption = C 1 - C 2 ⇒ Decrease in consumption = C 1 - 0.9126C 1 = 0.0874C 1 Percentage decrease in consumption = $$frac{{{ ext{Decrease in consumption}}}}{{{ ext{Initial consumption}}}} imes 100$$ ⇒ Percentage decrease in consumption = $$frac{{0.0874{{ ext{C}}_1}}}{{{{ ext{C}}_1}}} imes 100$$ ∴ The percentage decrease in consumption is 8.7% (correct to 1 decimal place)