A certain pair of used shoes can be repaired for $12.50 and will last for 1 year. A pair of same kind of shoes can be purchased new for $28.00 and will last for 2 years. The average cost per year of new shoes is what percent greater than the cost of repairing used shoes?
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Solution
Cost of repairing the used shoes = $12.5
28 Cost of new shoes for 1 year = \(\frac{28}{2}\) = $14
∴ 14 - 12.5 = $1.5 is extra average cost per year if new shoes are bought.
∴ Required percentage = \(\frac{1.5}{12.5}\) × 100 = 12%
In a certain school, 40 more than 1⁄3 of all students are taking a science course and 1⁄4 of those taking a science course are taking physics. If 1⁄8 of all students in school are taking physics, how many students are in the school?
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Solution
Let the number of students in the school be S.
∴ Number of students taking a science course = 40 + 1⁄3S
∴ Number of students taking physics course = 1⁄4( 40 + 1⁄3 s)
∴ S⁄8 = 1⁄4(40 +S⁄3) ∴ S = 2(40 + S⁄3)
∴ S = 80 + \(\frac{2S}{3}\) ∴ S = 240
30% of the students in a class were male students. Some of the students failed in examination. 45% of the students who failed were male. What was the ratio of failure rate %among male students to failure rate among female students?
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Solution
Let there be 100 students in a class.
∴ 30 were male and 70 were female.
Similarly, let × students fail.
∴ 0.45x were male students and 0.55x were female
∴ Failure rate among male = \(\frac{0.45x}{30}\)
Similarly, failure among female = \(\frac{0.55x}{70}\)
∴ Required ratio = \(\frac{\frac{0.45x}{30}}{\frac{0.55x}{70}}=\frac{45}{3}\times \frac{7}{55}=\frac{21}{11}\)
A man invests a total amount of $2000, some in bonds earning a 12% p.a. and some in fixed deposits earning 7% p.a. Find the amount invested in bonds if his total return on investments is $180.
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Solution
180 = x% of 2000 ∴ x=9%
By principle of allegation
∴ The ratio is 2 : 3
Money invested in bonds = 2⁄5 × 2000 = $800
Pinto travels at 6 kmph for x hours and 10 kmph for y hours. What is the minimum value of (x) if the average speed for (x + y) hours is 7 kmph, x and y are natural numbers.
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Solution
Average speed = \(\frac{Total\, distance\, travelled}{Total\, time\, taken}\)
∴ 7 = \(\frac{6x + 10y}{x+y}\)∴ 7x + 7y = 6x + 10y ∴ x = 3y
Since x and y are natural numbers, smallest value for y is 1 and corresponding smallest value for x = 3.
∴ x + y = 4 is the smallest possible value.
Half liter of hydrochloric acid of concentration 60% is mixed with 1 liter of hydrochloric acid of concentration 30%. One liter of water is added to the mixture. What is the percentage of water in .the mixture?
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Solution
∴ Percentage 0 water = \(\frac{1.9}{2.5}\)× 100 = 76%
A whole-seller offers successive discounts of 10% and x% on marked price which is 40% above cost price. What should be the approximate value of x so that whole-seller can make a profit of 10%?
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Solution
Let the C.P. be $100 ∴ Marked price = $140
Now, to make a profit of 10%, S.P. of article must be $110
∴ Discount offered = $30
10% of 140 = $14
∴ After first discount of 10% price of the article = $126.
Second discount has to be 126 - 110 = $16
∴ Percentage discount = \(\frac{16}{126}\) × 100 = 12.7 %
A sells a radio to B at 10% profit, B sells it to C at 10% profit. At what loss has ‘C’ sold it to D, if D had to pay same price as A has to pay?
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Solution
CP. for A = $100
∴ S.P. for A = CP. for B = $100+10 = $110
Also S.P. for B = CP. for C = 110 + 11 = $121
Now C sold it to D for $100
∴ C suffered a loss of $(121 -100) = $21
∴ Percentage loss to C = \(\frac{21}{121}\) × 100 ≈ 17.36%
A salesman works for all 365 days of the year. His monthly salary has a fixed component and a variable component. Variable component is directly proportional to the number of days salesman works. The difference between his salary for the month of January and February was $300. What should be his fixed component of salary so that he can get $9000 for the month of April? (The given year is not a leap year.)
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Solution
The salesman works for 31 days in January and 28 days in February.
∴ for 3 days he gets $300 i.e. per day $100 .
∴ Variable component for salary for April = 30 × 100 = $3000
∴ Fixed component = Total salary - $3000
= $9000 - $3000 = $6000
In a restaurant response time taken for an order is directly proportional to square of sums of all different letters of order placed by customer. Two friends Tom and Russell went to this restaurant. Tom ordered tea and pastry and Russell ordered coffee and cake. What is the ratio of response time for order of Tom to that of Russell?
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Solution
Number of different letters in Tom's order = 7 ⇒ [t, e, a, p, s, r, y)
Number of different letters in Russell's order = 6 ⇒ (c, o, I, e, a, k)
The ratio = (7⁄6)2 = \(\frac{49}{36}\)