Percentage - Study Mode
[#131] The shopkeeper increased the price of a product by 25% so that customer finds difficult to purchase the required amount. But Somehow the customer managed to purchase only 70% of the required amount. What is the net difference in the expenditure on that product ?
Correct Answer
(C) 12.5% less
Explanation
Solution: Let initially the quantity and rate be 100 each Quantity × rate = Expenditure 100 × 100 = 10000 Now, Increase in price is 25% and new quantity is 70% of original Quantity × rate = Expenditure 70 × 125 = 8750 Decreased expenditure, = 10000 - 8750 = 1250 % decrease $$ = frac{{1250 imes 100}}{{10000}} = 12.5\% $$
[#132] A customer asks for the production of x number of goods. The company produces y number of goods daily. Out of which z% are units for sale. The order will be completed in :
Correct Answer
(C) $$ {frac{{100x}}{{left( {100 - z}
ight)y}}} ,{ ext{days}}$$
Explanation
Solution: $$eqalign{
& { ext{Daily}},{ ext{supply}}, cr
& = left( {100 - z}
ight)\% ,{ ext{of}},y cr
& = frac{{ {left( {100 - z}
ight)y} }}{{100}} cr
& { ext{Thus,}},{ ext{required}},{ ext{number}},{ ext{of}},{ ext{days}} cr
& = {frac{{ {100x} }}{{left( {100 - z}
ight)y}}} cr} $$
[#133] In the Science City, Kolkata the rate of the ticket is increased by 50% to increased the revenue but simultaneously 20% of the visitor decreased. What is percentage change in the revenue. if it is known that the Science city collects one revenue only from the visitors and it has no other financial supports:
Correct Answer
(A) +20%
Explanation
Solution: Let the initial revenue be 100 100 === 50% ↑ (Ticket up) ===> 150 === 20% ↓ (Visitors down) ===> 120 There is 20% increase in the revenue
[#134] 600 students took the test on Physics and chemistry. 35% students failed in Physics and 45% students failed in chemistry and 40% of those who passed in chemistry also passed in Physics, then how many students failed in both :
Correct Answer
(D) 12
Explanation
Solution: Result Physics Chemistry Failed 35% 45% Passed 65% 55% Now, 55% of 600 passed in Chemistry = $$frac{{55 imes 600}}{{100}}$$ xa0 = 330 From question, 40% of those who passed in Chemistry(330 Students) also passed in physics = $$frac{{40 imes 330}}{{100}}$$ = 132, so, 132 students passed in both Therefore % who passed in both = $$frac{{132 imes 100}}{{600}} = 22\% $$ Passed in both subject = 22% of total students
% of students who passed in either Physics or Chemistry or both,
= (65 + 55) - 22 = 98%
Thus, percentage of students who failed in both subjects = 2%
Number of students who failed = 2% of 600 = 12
[#135] An alloy contains the copper and aluminum in the ratio of 7 : 4 While making the weapons from this alloy, 12% of the alloy got destroyed. If there is 12 kg of aluminum in the weapon, then weight of the alloy required is :
Correct Answer
(B) 37.5 kg
Explanation
Solution: Copper : Aluminum = 7 : 4
Let Copper and Aluminum in the weapon be 7x and 4x respectively
Given,
Aluminum in weapon = 12 kg So, → 4x = 12 → x = 3 Copper = 7x = 7 × 3 = 21 Kg. Total alloy in the weapon = 12 + 21 = 33 kg But 12% alloy get destroyed in making the weapon, i.e. 88% alloy is used in the weapon, so, → 88 % alloy = 33 kg → 100 % alloy = 37.5 kg