Q1. The simple interest accrued on an amount of Rs. 15500 at the end of three years is Rs. 5580. What would be the compound interest accrued on the same amount at the same rate in the same period?
(a) Rs. 6726.348
(b) Rs. 6276.384
(c) Rs. 6267.834
(d) Rs. 6627.438
Sol.
Rate of interest = (5580 × 100)/(15500 × 3) = 12%
After compounding 12% for 3 years, the equivalent rate of simple interest = 40.4928%.
Now, (12 × 3) = 36% = 5580
∴ 40.4918% = 5580/36 × 40.4928 = Rs. 6276.384
Q2. There are some parrots and some tigers in a forest. If the total number of animal heads in the forest are 858 and total number of animal legs are 1746, what is the number of parrots in the forest?
(a) 845
(b) 843
(c) 800
(d) None of these
Sol.
Let total no. of parrots and tigers in the forest are p and t respectively
A.T.Q.
P+t=858
2p+4t=1746
On solving these two equations
p=843
Q3. The length of a rectangle is twice the diameter of a circle. The circumference of the circle is equal to the area of a square of side 22 cm. What is the breadth of the rectangle if its perimeter is 668 cm?
(a) 24 cm
(b) 26 cm
(c) 52 cm
(d) Cannot be determined
Sol.
2(l + b) = 668
∴ l + b = 334
∴ l = (334 – b)
Length of a rectangle = Twice the diameter of a circle
334 – b = 2 × d = 2 × 2r = 4r
∴ r = (334 – b)/4
Area of square = Circumference of circle
(22)^2=2πr
484=(2×22(334-b))/(7×4)
∴ 334 – b = (484 × 7 × 4)/(2 × 22) = 308
∴ b = 334 – 308 = 26 cm
Q4. The arithmetic mean of the following numbers is
1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7
(a) 4
(b) 5
(c) 14
(d) 20
Sol.
required mean
=(1×1+2×2+3×3+4×4+5×5+6×6+7×7)/(1+2+3+4+5+6+7)
=(1+4+9+16+25+36+49)/28
=140/28=5
Q5. If the average of 6 consecutive even numbers is 25, the difference between the largest and the smallest number is:
(a) 18
(b) 10
(c) 12
(d) 14
Sol.
Let, the numbers be x, x + 2, …, x + 10
∴ Required difference = x + 10 – x = 10
Q6. The average age of the family of 5 members is 24. If the present age of youngest member is 8 years, then what was the average age of the family just before the birth of the youngest member?
(a) 20 years
(b) 16 years
(c) 12 years
(d) 18 years
Sol.
Total age of the family of five numbers
= 24 × 5 = 120
Total age of the family of 5 members before 8 years
= 120 – 5 × 8
= 120 – 40 = 80
So, the required average age = 80/4 = 20 years.
Q7. A man spends on an average Rs. 269.47 for the first 7 months and Rs. 281.05 for the next 5 months. Find out his monthly salary if he saved Rs. 308.46 during the year.
(a) Rs. 400
(b) Rs. 500
(c) Rs. 300
(d) Rs. 600
Sol.
Total spending in 12 months
= Rs [269.47 × 7 + 281.05 × 5]
= Rs. 3291.54
Total income = spending’s + savings
= Rs. 3291.54 + Rs. 308.46
= Rs. 3600.00
∴ Monthly salary = Rs. 3600/12 = Rs. 300.
Q8. Three years ago the average age of a family of 5 members was 17 years. With the birth of a new baby, the average remains the same even today. Find out the age of the baby.
(a) 1 year
(b) 3 years
(c) 2.5 years
(d) 2 years
Sol.
Present age of 5 members
= (5 × 17 + 3 × 5) years.
= 100 years
Present age of 5 members and a baby
= 17 × 6 = 102 years.
∴ Age of the baby = (102 – 100) years.
= 2 years.
Q9. A batsman in his 17th innings, makes a score of 85 runs, and thereby, increase his average by 3 runs. What is his average after the 17th innings? He had never been ‘not out’.
(a) 47
(b) 37
(c) 39
(d) 43
Sol.
Average score before 17th innings
= 85 – 3 × 17 = 34
∴ Average score after 17th innings
= 34 + 3 = 37.
Q10. The average salary of 20 workers in an office is Rs. 1900 per month. If the manager’s salary is added, the average becomes Rs. 2000 per month. The manger’s annual salary (in Rs.) is-
(a) 24000
(b) 25200
(c) 45600
(d) None of these
Sol.
Total monthly salary of 21 persons
= Rs. (21 × 2000) = Rs. 42000
Total monthly salary of 20 persons
= Rs. (20 × 1900) = Rs. 38000
Monthly salary of the manager = Rs.4000
Annual salary of the manager = Rs. 48000
