## Tuesday, 21 June 2016

### Night Class: Quant Quiz

1. Each side of an equilateral triangle is increased by 20%. The percentage increase in its area is-
1) 44%
2) 42%
3) 40%
4) 46%
5) None of these

2.The length of a rectangular plot is 15 metres. If the cost of cultivating the plot at Rs. 13.20 per metres^2 is Rs. 5346. Find the breadth of plot.
1) 23 m.
2) 25 m.
3) 27 m.
4) 29 m.
5) 30 m.

3. A cistern is constructed to hold 300 litres, and the base of the cistern is one square meter. What is the depth of the cistern? (A cubic metre is equal to 1000 litres.)
1) 35 cm.
2) 30 cm.
3) 40 cm.
4) 45 cm.
5) None of these

4. How many cubic metres of the earth must be dug out to sink a well 22 m. deep. If the cost of plastering the inner surface of the wall at Rs. 23.5 per square meter is Rs. 22748.
1) 8338 m^3
2) 3838 m^3
3) 3883 m^3
4) 3388 m^3
5) None of these

5. Find the slant height of a cone whose volume is equal to 3080 m^3 and the diameter of whose base is 28 m. (Ans. in approx. value)
1) 18.5 m
2) 20.5 m
3) 23.5 m
4) 26.5 m
5) 29.5 m

6. The probability that a leap year selected at random will contain either 53 Monday or 53 Tuesday is-
1) 1/7
2) 2/7
3) 3/7
4) 4/7
5) None of these

7. A book contains 1000 pages. A page is chosen at random. The probability that the sum of the digits of the marked number on the page is equal to 9.
1) 19/200
2) 17/200
3) 13/200
4) 11/200
5) None of these

8. If the difference between CI and SI on a certain sum of money for 3 years at 8% per annum is Rs. 308, find the sum.
1) Rs. 15562
2) Rs. 16255
3) Rs. 15625
4) Rs. 16525
5) None of these

9. The simple interest on sum of money will be Rs. 200 after 4 years. In next 8 years principal be comes tripled. What will be the total interest at the end of the 12 year?
1) Rs. 1200
2) Rs. 1400
3) Rs. 800
4) Rs. 1000
5) None of these

1. 1
Reqd % increase = 2 * 20 + 20^2/100 = 144%

2. 3
Total Area = 5346/13.2 = 405 m^2
Breadth = 405/15 = 27 m

3. 2
1 sq m * Depth = 300/1000 = 3/10

Depth = 3/10 m
= 3/10 * 100 = 30 cm

4. 4
Inner Surface Area = 22748/23.5 = 968 sq m
2 * 22/7 * r *h = 968
2 * 22/7 * r * 22 = 968
r = (968 * 7)/(2 * 22 * 222) = 7 m

Volume of the earth dug ut = Volume of the well = 22/7 * 7 * 7 * 22 = 3388 cum

5. 2
Volume of the cone = 1/3 * 22/7 * r^2 * h
1/3 * 22/7 * 14 * 14 * h = 3080
h = (3080 * 3 * 7)/(14 * 14 * 22) = 15 m
Slant height = √{(14)^2 + (15)^2}
= 20.5 m

6. 3
In a leap year 366 day or, 52 week and 2 days. these 2 days will be
1. Sunday and Monday
2. Monday and Tuesday
3. Tuesday - Wednesday
4. Wednesday - Thursday
5. Thursday - Friday
6. Friday-Saturday
7. Saturday - Sunday
Required Probability = 3/7

7. 4; The number of numbers whose sum is 9 is
one digit number = 1
Two digit number = 9
Three digit number = 9 + 8 + 7 + ...... + 1 = (9 * 10)/2 = 45

Required Probability = (1 + 9 + 45)/1000 = 55/1000 = 11/200

8. 1

Sum = {Difference * (100)^3}/ r^2 (300 + r) = (308 * 100 * 100 * 100)/(64 * 308) = Rs. 15625

9. 2
SI = PTR/100
200 = (P * r * 4)/100
4Pr = 200 * 100
SI = (3P * r * 8)/100 = (3 * 2 * 4Pr)/100
= (6 * 200 * 100)/1000 = Rs. 1200

Total Interest = Rs. 1200 + Rs. 200 = Rs. 1400