Percentage - Study Mode

[#196] If x, y, z are three positive integers such that x is greater then y and y is greater than z, then which of the following is definitely true ?
Correct Answer

(D) All of these

Explanation

Solution: (a) x% of y = $$frac{xy}{100}$$ and y of z = $$frac{yz}{100}$$ x > y, y < z ⇒ xy > yz ⇒ $$frac{xy}{100}$$ > $$frac{yz}{100}$$ ⇒ x% of y > y% of z (b) y% of x = $$frac{xy}{100}$$ and z% of y = $$frac{yz}{100}$$ As proved above, y% of x > z% of y (c) z% of x = $$frac{xy}{100}$$ and y% of z = $$frac{yz}{100}$$ x > y ⇒ xz > yz ⇒ $$frac{xz}{100}$$ > $$frac{yz}{100}$$ ⇒ z% of x > y% of z

[#197] If the length of a rectangle is increased by 12% and the breadth is decreased by 8%, the net effect on the area is:
Correct Answer

(A) increase by 3.04%

Explanation

Solution: $$eqalign{
& 12\% o frac{{ + 3}}{{25}} cr
& 8\% o frac{{ - 2}}{{25}} cr
& { ext{Length}} o 25:28 cr
& underline {{ ext{Breadth}} o 25:23} cr} $$ $${ ext{Increase }}\% = frac{{19}}{{625}} imes 100 = 3.04\% $$

[#198] Raju, Ravi and Ashok contested an election. 5% votes polled were invalid. Raju got 30% of the total votes. Ravi got 32% of the total votes. The winner got 5136 more votes than the person who received the least number of votes. Find the total number of votes polled.
Correct Answer

(A) 171200

Explanation

Solution: Let total vote = 100 Invalid vote = 5 Raju got = 30 Ravi got = 32 Ashok got = 95 - (30 + 32) = 33 33 - 30 = 3 unit → 5136 1 unit → $$frac{{5136}}{3}$$ 100 unit → 171200

[#199] A certain number of student from school X appeared in an examination and 30% student failed. 150% more students than more from school X, appeared in the same examination from school Y, If 80% of the total number of students who appeared from X and Y passed, then what is the percentage of student who failed from Y?
Correct Answer

(C) 16

Explanation

Solution: Calculation: 30% of the students from school X failed Let the number of students from school X be 100 ⇒ Number of students who failed = 30 ⇒ Number of students who passed = (100 - 30) = 70 According to the question, 150% more students than school X, appeared in the examination from school Y Number of students from school Y = $$100 + left( {100 imes frac{{150}}{{100}}}
ight)$$ ⇒ Number of students from school Y = 250 Again, according to the question, 80% of the total number of students from X and Y passed Total students from school X and Y = 100 + 250 = 350 ⇒ Total number of students who passed = $$350 imes frac{{80}}{{100}}$$ ⇒ Total number of students who passed = 280 Now, Number of students who passed from school Y = 280 - 70 ⇒ Number of students who passed from school Y = 210 Number of students who failed from school Y = 250 - 210 ⇒ Number of students who failed from school Y = 40 Percentage of students who failed from Y = $$frac{{40}}{{250}} imes 100$$ ⇒ Percentage of students who failed from Y = 16% ∴ 16% of students failed from school Y.

[#200] When an article is sold at 5% discount, then there is a profit of 14%. If the discount is 11%, then what will be the profit?
Correct Answer

(A) 6.8%

Explanation

Solution: Given: For Discount = 5%, Profit = 14% Formula used: Selling price = Marked price - Discount Cost price = $$frac{{100}}{{100 + { ext{Profit}}}} imes { ext{Selling price}}$$ Profit % = $$frac{{{ ext{Selling price}} - { ext{Cost price}}}}{{{ ext{Cost price}}}} imes 100$$ Calculation: Let the Marked price of the article = Rs. 100 Discount = 5% ⇒ Selling price = Rs. 95 Profit = 14% ⇒ Cost price = $${ ext{Rs}}{ ext{. }}left( {frac{{100}}{{100 + 14}}}
ight) imes 95$$ Cost price = $${ ext{Rs}}{ ext{. }}frac{{250}}{3}$$ xa0= Rs. 83.3 For the Discount of 11%, Selling price = Rs. 89 Then Profit % = $$frac{{89 - 83.3}}{{83.3}} imes 100$$ Profit = 6.84 ≈ 6.8 Hence, the correct answer is option A.