Q1. The sum of five consecutive even numbers is equal to 170. What is the sum of the second largest number amongst them and the square of the smallest number amongst them together?
(a) 940
(b) 932
(c) 938
(d) 934
(e) None of these
Sol. Let the five consecutive even numbers are 2x, 2x + 2, 2x + 4, 2x + 6, 2x + 8 respectively.
According to the question,
2x + 2x + 2 + 2x + 4 + 2x + 6 + 2x + 8 = 170
10x + 20 = 170
10x = 150
x= (150/10) = 15
Thus, the five numbers are 30, 32, 34, 36, 38 respectively.
Therefore, required sum =(30)^2+36 = 900+36 = 936
Q2. The area of a square is four times area of a rectangle. The length of the rectangle is 25 cm and its breadth is 1 cm less than one-fifth its length. What is the perimeter of the square?
(a) 40 cm
(b) 80 cm
(c) 160 cm
(d) Cannot be determined
(e) None of these
Sol. Length of the rectangle = 25cm
Thus, Breadth = [(1/5)*Length] - 1 = (25/5)-1 = 4cm
Given, area of the square = 4*area of the rectangle
(side)^2 = 4*(25*4)
side = 20cm
Hence, perimeter of the square = 4*side = 4*20 = 80cm
Q3. Sohan got 54 marks in Hindi, 65 marks in Science, 89 marks in Maths, 69 marks in Social Science and 68 marks in English. The maximum marks of each subject are 100. How much overall percentage of marks did he get?
(a) 74
(b) 69
(c) 68
(d) 72
(e) None of these
Sol. Marks in all subjects = 54 + 65 + 89 + 69 + 68 = 345
Total maximum marks = 5 * 100 = 500
Thus, required percentage =(345/500)*100=69%
Q4. 8 women cam complete a piece of work in 15 h. In how many hours will 12 women complete the same piece of work?
(a) 12
(b) 6
(c) 8
(d) 10
(e) None of these
Sol. 8 women can complete a piece of work in = 15 h
1 woman can complete a piece of work in = (15 * 8) h = 120 h
Thus, 12 women can complete a piece of work in =120/12 = 10 h
Q5. The length of a rectangle is 24 cm which is 10 cm more than the diameter of a circle. What is the area of the circle?
(a) 210 sq cm
(b) 176 sq cm
(c) 132 sq cm
(d) 154 sq cm
(e) None of these
Sol. Diameter of a circle = 24 - 10 = 14 cm
Radius of a circle =14/2 = 7 cm
Area of a circle = (22/7)r^2 = (22/7)*7*7 = 154 sq.cm
Q6. Three substances A, B and C are mixed together. Their volumes are proportional to 4, 3 and 2 respectively and the weights of equal volumes are proportional to 5, 4 and 3 respectively. What is the weight of substance A if the weight of the mixture is 114 kg?
(a) 30 kg
(b) 40 kg
(c) 50 kg
(d) 60 kg
(e) 70 kg
Sol. Let the volumes of A, B and C be 4, 3 and 2.
And the weight of equal volumes of A, B and C be 5, 4 and 3
Ratio of weight of A, B and C = 5*4 : 3*4 : 2*3
= 20 : 12 : 6
= 10 : 6 : 3
So, Weight of A = 10/19 * 114 = 60kg
Q7. How many numbers lying between 3000 and 4000 and divisible by 5 can be made with the digits 3, 4, 5, 6, 7 and 8? (The digits are not to be repeated in any number).
(a) 10
(b) 12
(c) 14
(d) 16
(e) 18
Sol. Every number between 3000 to 4000, which is divisible by five and which can be formed by the given digits, must contain 5 at unit’s place and 3 at thousand’s place.
Thus we are left with four digits out of which we are to place two between 3 and 5, which can be done in
4P2 = 12 ways
Q8. A student scored 20% of maximum marks and failed by 26 marks and when he scores 40% of the marks in the same paper he passes by 14 marks. Then find the maximum marks?
(a) 100
(b) 200
(c) 300
(d) Cannot say
(e) None of the above
Sol. Let the maximum marks be M, then (40 – 20) % of maximum marks will equal to 26 + 14 = 40 marks.
Therefore 20% * M = 40 or M = 200
Q9. Ram could save 20% of his income. But two years later when his income is increased by 10%, he could save the same amount only as before. By how much percent has his expenditure increased?
(a) 12.5
(b) 11.11
(c) 9.09
(d) 15
(e) None of the above
Sol. Let original income = Rs. 100. Then, saving = Rs. 20 and expenditure = Rs. 80
New income = Rs. 110, New saving = Rs. 20
New expenditure = Rs. 90
Increase in expenditure = Rs. 10.
Thus, Increase % = [10/80)*100]% = 12.5%
Q10. Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q’s age?
(a) 1 year
(b) 2 years
(c) 25 years
(d) Data inadequate
(e) None of these
Sol. R – Q = R – T => Q = T. Also, R + T = 50
R + Q = 50
So, (R – Q) cannot be determined.
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