A contractor employs 8 men,S women and 12 children and finishes a piece of work in one day. A woman does double the work a man does and a child does half the work a man does. If only women were employed, which of the following gives the number of women and number of days required by those women to complete the work?
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Solution
Ans: (A, B, C, D)
Work done by 1 woman in 1 day = 4w.
Work done by 1 man in 1 day = 2w.
Work done by 1 child in 1 day = w.
∴ Work content in terms of win 1 day
= 8(2w) + 5(4w) + 12w = 48w
Work done by 1 woman in 1 day = 4w Hence the product of number of women and days required should be \(\frac{48}{4}\) = 12
In Robert’s garden, (m + 2) mango trees yield 60 mangoes per year, m trees yield 120 mangoes per year and (m – 2) trees yield 180 mangoes per year. Which of the following could be the average yield per year per tree?
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Solution
Ans: (B, D, E)
Total number of mangoes from all trees
= 60(m + 2) + 120m + 180(m - 2)
= 60m + 120 + 120m + 180m - 360
= 360m -240
Total number of mango trees = m + 2 + m + m- 2 = 3m
∴ verage = \(\frac{Total\, number\, of\, mangoes}{Total\, number\, of\, mango\, trees}\)
∴ x = \(\frac{360m - 240}{3m}\) ∴ 3mx = 360m - 240
∴ Check with different values of x, m should be an integer
Susan gave 2⁄5 of the amount she had to Julie. Julie in turn gave half of what she received from Susan to Michelle. If the difference between the amount remaining with Susan and that received from Julie by Michelle is at the most $800, how much money did Susan had in the beginning?
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Solution
Ans: (A, B, D, E)
Let Susan have $x with her in the beginning.
she gives $\(\frac{2x}{5}\)to Julie.
∴ She has $\(\frac{3x}{5}\) remaining with her.
Julie gives $x⁄5 to Michelle.
∴ Difference \(\frac{3x}{5}-\frac{x}{5}\) $ $800
∴ \(\frac{2x}{5}\)≤$ $800 ∴x ≤ $2000
Susan had at the most $2000 in the beginning.
Henry and Lucy are partners in business. They earn profit in the ratio of the capital used. Henry contributes 5% of the total capital for each of the x months of a year.
Lucy contributes the balance in the remaining months. If Lucy’s contribution per month is y%, then possible values of x and y are
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Solution
Ans: (A, C, D)
Let total contribution = 100
Henry's Share will be 5x. Lucy's Share will be 100-5x
∴ Lucy's Share per month will be y = \(\frac{100-5x}{12-x}\)
The percentage profit earned by John in selling a watch for $1920 is equal to the percentage loss incurred by him in selling the same watch at $1280. At what price watch must he sell to earn at least 25% profit?
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Solution
Ans: (C, E)
Let the Cost Price of the watch be $x.
Since the percentage of profit on cost and percentage of loss on cost is same, the amount of profit and loss will also be equal.
∴ 1920 - x = x - 1280
∴ 2x = $3200 ∴.x = 1600
∴ Cost Price of watch = $1600
125 At 25% profit, the selling price = 1600 × \(\frac{125}{100}\)= $2000 more to get more than 25% profit
ABC road builders undertook to do a certain piece of work in 9 days. They employed a certain number of men. But because of commutation problems, 6 men remained absent from the first day itself. The rest could finish the work in 15 days. Find the number of men originally employed?
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Solution
Ans: (B)
Let the number of men originally employed be m.
∴ m - 6 men actually worked for 15 days and finished the job.
Work content = (m - 6) × 15 men days.
The same work can be completed by m men working for 9 days.
∴ 9m = 15(m -6) ∴ 9m = 15m -90 ∴ m = 15
Clark, an oil trader, bought 2 kinds of machine oil, type A and type B at $46 and $62 per kg respectively. How many kg of type A should be mixed with type B to get a mixture of 15kg so that by selling the mixture at $54 per kg, he is in profit.
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Solution
Ans: (A, B, D)
The selling price 54$ is the average of the two prices 46$ and 62$. Hence to be in profit, the oil with lower cost should be more than half. Hence oil A should be mixed more than 7.5 kg
which of the following will be equal to 2 50 ?
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Solution
Answer: A, B, E
For option A: 32 = 25, hence (-32)10 = (25)10 = 250 hence this is correct
Option B: 16 = 24 and 4 = 22, hence 1610 /4(-5) = 240 / 2(-10)= 250.
Hence it is correct
Option C: 650 = 250 × 350 hence 650 /310 = 250 × 340 hence not correct
Option D: 1050 = 550 × 250 hence 550 / 1050 = 2(-50)hence not correct
Option E: 32 = 25 hence (325)2= (2)(5)(5)2= 250 hence correct
0 is the centre of the circle, A and B lie on the circle.· What are the possible values of x and y. Mark one or more correct answers:
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Solution
Answers: B, C, E
In the given triangle, OA and OB are equal hence the angle of the triangle are x, x, y. Hence 2x + y = 180°.
The options which satisfy this equation are B, C, E.
Hence those are the correct options
For any integer n the expression n3 + n2 + 1 can possibly be?
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Solution
Ans: Option A, C, D
Expression is n3 + n2 + 1
1) Consider n = 0 ∴ n3 + n2 + 1 = 1 → odd
2) Consider n = 23 + 22 + 1= 13 → Prime
For value of n greater than 2, the value of the expression is either odd or prime or composite but never even.