1.The breadth of a rectangular hall is three-fourths of its length. If the area of the floor is 768 sq.m. then the difference between the length and breadth of the hall is :
(1) 8 meters
(2) 12 meters
(3) 24 meters
(4) 32 meters
2.A is thrice as good as workman as B and therefore, able to finish a job in 60 days less than B. Working together they will do it in:
(1) 20 days
(2) 22 1/2 days
(3) 25 days
(4) 30 days
3.Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. If both pipes are opened together, the time taken to fill the tank is:
(1) 50 minutes
(2) 12 minutes
(3) 25 minutes
(4) 15 minutes
4.If a man walks 20 km at 5 km/hr, he will be late by 40 minutes. If he walks at 8 km per hr, how early from the fixed time will he reach?
(1) 15 minutes
(2) 25 minutes
(3) 50 minutes
(4) 11/5 minutes
5.The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr Another train starts from B at 9 a.m. and travels towards A at 75 km/hr at what time do they meet?
(1) 10 a.m.
(2) 10 : 30 a.m.
(3) 11 a.m.
(4) 11 : 30 a.m.
6.If AB is chord of a circle. P and Q are the two points on the circle different from A and B, then :
(1) The angles subtended at P and Q by AB are always equal.
(2) The sum of the angles subtended by AB at P and Q is always equal to two right angles
(3) The angles subtended by AB at P and Q are either equal or supplementary
(4) The sum of the angles subtended at P and Q is four right angles
7.A person who spends 66 2/3% of his income is able to save Rs. 1,200 per month. His monthly expenses (in Rs) is :
(1) 1,200
(2) 2,400
(3) 3,000
(4) 3,200
8.If cos 2x = cos 60° cos 30° + sin 60° sin 30°, then x is :
(1) 10°
(2) 15°
(3) 30°
(4) 45°
9.Applied to a bill for Rs. 1, 00, 000 the difference between a discount of 40% and two successive discounts of 36% and 4% is:
(1) Nil
(2) Rs. 1, 440
(3) Rs. 2,500
(4) Rs. 4, 000
10.Compound interest (compounded annually) on a certain sum of money for 2 years at 4% per annum is Rs. 102. The simple interest on the same sum for the same rate and for the same period will be:
(1) Rs. 99
(2) Rs. 101
(3) Rs. 100
(4) Rs. 98
Answer and Solution:
(1) Let the length of rectangular hall = xm
Breadh = 3/4 * xm
we know that Area of rectangular = Length * Breadth
= x * 3/4 x sq.m = 3/4 x^2 m^2
According to question.
3/4 x^2 = 768
x^2 = (768 * 4) / 3
or, x = √((768 ×4)/3) = 32m
Lenth = 32 cm and Breadh = 24 m
Required difference = 32 - 24 = 8m
(2) Let A can finish the whole work in x days
so B can finish the same work in 3x days.
According to question.
3x - x = 60
so x = 30 days
so A can finish the work in 30 days and B can finish the same work in 90 days.
so (A + B)'s one day's work = 1/30 + 1/90 = 4/90
so (A + B)'s can finish the complete work in = 90/4 = 22 1/2 days.
3.(2) Required time = 1/(1/20+ 1/30)= (20 ×30)/50 = 12 minutes
4.(3) Time taken to cover 20 km at the speed of 5km/hr = 4 hours.
Fixed time = 4 hours - 40 minutes = 3 hours 20 minutes
Time taken to cover 20 km at the speed of 8 km/hr
= 20/8 = 2 hours 30 minutes
Required time = 3 hours 20 minutes - 2 hours 30 minutes = 50 minutes
5.(3) Distance travelled by first train in one hour = 60 * 1 = 60 km
A--------------------------------------B
300km
Therefore, distance between two train at 9 a.m.
= 330 - 60 = 270 km
Now, Relative speed of two trains = 60 + 75 = 135 km/hr
Time of meet of two trains = 270/135 = After 2 hrs.
Therefore,both the trains will meet at 9+2= 11A.M.
6.(3) There are two possibilites :
Case I. When P and Q are on the same side of AB. In this case ∠APB= ∠AQB (angles in the same segment)
Cast II. When P and Q are on the opposite side of AB. In this case PAQB is a cycle quadrilateral.
So, ∠APB+ ∠AQB=180°
7.(2) Saving = 100% - 66 2/3%
= 33 1/3%
so 33 1/3% = Rs. 1200
so 100% = 1200/100 * 3 * 100
Rs. 3600
so Expenses = 3600 - 1200
= Rs. 2400
8.(2) cos 2x = cos 60° cos°30° + sin 60° sin 30°
= cos (60° - 30°)
= cos 2x = cos 30°
= 2x = 30 = x = 15°
9.(2) Successive discount of 36% and 4%
= {36 + 4 - (36*4)/100}%
= 38.56%
Difference = 40 - 38.56
= 1.44%
10.(3) Let principal be Rs. P
According to question.
102 = p {(1+r/100)^t- 1}
Where r = 4% and t
= 2 years
P = 102/((26/25)^2- 1)=Rs.1250
so Simple Interest at rate of 4% for 2 years
= (1250 ×4 ×2)/100=Rs.100
Required answer is Rs. 100
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