In an experiment certain numbers of balls are being distributed in a certain number of urns. If 3 balls are put in each urn, then 3 ball becomes excess, and if 4 balls are put in each urn, then 1 urn becomes excess. How many balls are there?

Solution

Let number of balls be 'b' and number of urn be 'u'

∴ 3u + 3 = b → Condition 1

4(u -1) = b → Condition 2

∴ 3u + 3 = 4u - 4

∴ u = 7 ∴ b = 24

P is an odd number. What is the remainder when p³ – P + 1 is divided by 24?

Solution

Put different values for P

P = 1 ⇒ p³ - P + 1 = 1 ∴ Remainder = 1

P = 3 ⇒ p³ - P + 1 = 25 ∴ Remainder = 1

P = 5 ⇒ p³ - P + 1 = 121 ∴ Remainder = 1

An empty fuel tank of car was filled with ‘A’ type of petrol. After driving some distance, the tank became half empty; it was filled with ‘B’ type of petrol. Again after driving some distance, tank was half empty and it was filled with ‘A type of petrol. Again after driving some distance, tank was half empty and it was filled with ‘B’ type of petrol. Now what is the percentage of ‘A’ type of petrol in the tank?

Solution

John went to market with $100. If he buys 3 pen and 6 pencils he uses up all his money. On the other hand if he buys 3 pencils and 6 pens, he would fall short by 20%. If he wants to buy equal number of pens and pencils, how many pencils can he buy?

Solution

Let 'x' and 'y' denote pens and pencils respectively. John has $100. He can buy 3 pens and 6 pencils from $100. ∴ 3x + 6y = 100

If he buys 6 pens and 3 pencils, he is short of 20% of the price.

∴ Price must be $125.

∴ 6x + 3y = 125

Adding both the equations

∴ 9x + 9y = 225 ∴ x + y = 25

∴ He can buy 4 pens and 4 pencils from $100.

In a hotel management entrance examination, there are 200 questions with four alternatives each. A student marks first alternative as answer to all questions. What is his probable net score if each right answer fetches +1 and each wrong answer fetches –¹⁄₄ marks?

Solution

Probability that alternative is correct = ¹⁄₄ and that it is ³⁄₄.

∴ Probable score = 1(¹⁄₄ × 200) - ¹⁄₄(³⁄₄ × 200)

= 50 - 37.5 = 12.5

What is the value of (0.00032)^0.6?

Solution

$\left ( \frac{32}{100000} \right )^{\frac{6}{10}}=\left ( \frac{32}{100000} \right )^{\frac{3}{5}}=\left ( \sqrt[5]{\frac{32}{100000}} \right )^{3}$

∴ $\left ( \frac{2}{10} \right )^{3}=\left ( \frac{8}{100} \right )=.008$

In the above figure, square PQRS is divided into 5 equal parts, all of same area, central part is circular. If PQ = 110 cm., what is radius of circle in cm?

Solution

$Area\, of\, circle=\frac{Area\, of\, square}{5}$

∴ $\frac{22}{7} \timesr^{2}= \frac{110 \times 110}{5}$

∴ r² = 110 x 7 = 770 ∴r = 28 cm. (approx.)

A boat covers a distance of 30 kms. downstream in 2 hours while it takes 6 hours to cover the same distance upstream. What is the speed of boat in kms per hour?

Solution

Speed of boat is x and speed of the stream is y.

Distance upstream and downstream is the same.

Speed downstream is x + y and upstream is x - y.

2(x + y) = 6(x - y)

∴ 2x + 2y = 6x - 6y ∴x = 2y

Now $\frac{30km}{x+y}$ = 2 hours. Substituting x = 2y

$\frac{30}{2y+y}=2$ ∴ y = 5 ∴ x = 10

Ajar full of wine weighs 1 kg. and a half full jar weighs ³⁄₄ of kg. What fraction of the weight of jar is the weight of wine when the jar is half full of wine?

Solution

J + W = 1 kg..........(I)

J + ¹⁄₂W = ³⁄₄kg...........(II)

Subtracting II from I

¹⁄₂W = ¹⁄₄Kg.

∴ J = ¹⁄₂Kg.

∴ Ratio of weight of wine half full of Jar and weight of Jar is = $\frac{\frac{1}{4}}{\frac{1}{2}}=\frac{1}{2}$

George’s father will be twice his age 6 years from now. His mother was twice his age 2 years ago. If George’s age is 22, what is the difference between his fathers and mother’s ages?

Solution

George's present age = 22

∴ His age 6 years hence = 22 + 6 = 28.

∴ His father's age 6 years hence = 28 × 2 = 56.

∴ Father's present age = 56 - 6 = 50 years.

George was 20 years old 2 years back.

∴ His mother's age 2 years before = 20 × 2 = 40.

∴ His mother's present age = 42 years.

∴ Difference = 40 - 42 = 8 years .

Attempted

0

Correct

0

Wrong

0

Complete

Attempted

Wrong

Correct