In a certain summer camp for children, 57% of the kids that enrolled opted for playing Football, 28% for Baseball and remaining for other games. If 79% of all the kids enrolled, opt for Chess, what is the least possible percentage of kids playing baseball that opt for Chess?

Solution

Let there be 100 kids in the camp.

∴ 57 opt for Football, 28 for Baseball and 100 - (57 + 28) = 15 opt for other games.

To satisfy the given condition, maximum number of Football playing children and kid playing other games must opt for Chess.

Baseball playing kids that must opt for Chess = 79 - (57 + 15) = 7

∴ Required % = $\frac{7}{28}$ × 100 = 25%

The price of postage stamps has increased 5 cents per year since 1990. If 10 stamps were purchased every year from 1998 to 2000, total cost would be $35. How much did a stamp cost in 1995?

Solution

Price of stamp in 1998 is X cents

∴ Total cost of stamps in 1998,1999 and 2000 will be 10 (X + X + 5 + X + 10) = 10 (3X + 15)

= 30X + 150

30X + 150 = 4500

∴ X = 145

∴ Price of stamp in 1995 will be 145 - 5 - 5 - 5 = 130 Cents

Linda deposits a bag of dimes and quarters into her bank account. If the teller tells her to deposit total of 30 coins worth $ 4.50, then find the number of quarters? (1 dime = 10 cents, 1 quarter = 25 cents)

Solution

Let q be the number of quarters and d be the number of dimes.

∴ d + q = 30 (I)

The value of dimes and quarters can be expressed as

O.1 d + 0.25q = 4.50

∴ 10d + 25q = 450 (II)

Multiplying (I)by 10 and subtracting it from (II)

15q = 150 ∴ q = 10 ∴ d= 20

A is a set of integers between 1 and 100 (both inclusive) that are not divisible by 7. B is a set of integers between 1 and 100 (both inclusive) that are not divisible by 9. How many elements will there be in A U B?

Solution

First we will have to find out integers divisible by 7 or by 9 or by both.

Integers divisible by 7 are 14

Integers divisible by 9 are 11

∴ Total integers divisible by 7 or 9 = 25

Integer divisible by 7 arid 9 (i.e. 63) is only 1

∴ Integers divisible by 7 or by 9 or by both =25-1 =24

∴ 100 - 24 = 76 integers are neither divisible by 7 nor by 9

Machine P can produce ‘k’ units in ³⁄₅ of the time it takes machine Q to produce ‘k’ units. Machine Q produce ‘k’ units in ¹⁄₃ of the time it takes machine R to produce ‘k’ units. If all machines work independently for the same time, then fraction of the total output is produced by machine Q and R together is?

Solution

If R can produce K units in 60 min, Q will produce K units in 20 min arid P can produce K units in 12 min,

∴ If all 3 persons work for 60 min R will Produce 1K, Q will produce 3K arid P will produce 5K.

∴ Total production is 9K

Q arid R will produce ⁴⁄₉ units

Mark buys some raw material and makes a finished product after processing. He marks up the price by 25% and sells it to Linda. Linda improves the product by spending 20% of her cost and sells it to Joe at a profit of 20% on cost price. Joe spends ¹⁄₆ of what the product cost him and sells it at a profit of 10%.Selling price of Joe is what percentage greater than the cost price of Mark?

Solution

Tabulate the data

Selling price of Joe IS 131 % more than cost of Mark.

In a certain family, 12 times the number of children is greater by 12 than thrice the square of the number of children. How many children are there?

Solution

Let the number of children be x.

∴ 12x = 3x² + 12 ∴ 3x² - 12x + 12 =0

∴ x² - 4x + 4 = 0 ∴ (X-2)² = 0 ∴ x = 2

In an examination, 59% students passed in Sociology, 55% passed in Psychology and 18% failed in the examination. 160 students passed in both the subjects. Find total number of candidates.

Solution

18% failed in the examination.

∴ 82% have passed.

∴ 82% = 59% + 55% - common in both.

∴ 32% have passed in Sociology as well as Psychology.

32% = 160 students.

Total candidates are 100% = 500

23% of 500 = 115 passed only in Psychology.

In how much time can a train 1200 meters long running at 36 kmph cross a stationary train 600 meters long standing on a stationary platform 200 m long?

Solution

Distance travelled by the train in completely crossing the other train is equivalent to the sum of its own length arid that of other train.

$Time=\frac{Distance}{Speed}=\frac{200 + 600}{36000}\times 60$ min = 3 min

Length of platform is not important in this problem.

The price of tomatoes and potatoes is increased by 13% each. The price per pound of tomatoes has increased by $1.43 and the price of potatoes is increased by $0.91, then the difference between the price of tomatoes and potatoes is what fraction of the price of potatoes?

Solution

The price of tomatoes $\frac{143 \times 100}{13}= 1100$ cents

similarly, the price of potatoes $\frac{91 \times 100}{13}= 700$ cents

∴ Difference in values = 400 cents

Require fraction = $\frac{400}{700}$ = ⁴⁄₇

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