Ques1)
A group of students decided to buy a tape recorder from 170 to 195 rupees.. But at the last moment two students backed out of the decision so that the remaining students had to pay one rupee each more than they had planned. What was the price of the tape recorder if the students paid equal share?
a) 200
b)180
c) 160
d)140
Answer : (b)
Explanation :let the price of the tape recorder be Rs.x and let there be n students in the group.
Then ,the contribution made by each student in two cases are Rs. x/n and x/n-2 respectively.
It is given that
Then
X= n2 – 2n divided by 2
Now 170 ≤ x ≤ 195 , substitute x
340≤ n2 – 2n ≤ 390
340+1 ≤ n2 – 2n +1 ≤ 390+1
341 ≤ (n-1)2 ≤ 391
19.4 ≤ n ≤ 20.7
N=20
Because n is a natural number
Price of the tape recorder (x) = n2 – 2n / 2
X= (20)2 – 20 / 2
x= Rs.180
Ques 2)
A work is completed by 3men in a day. The same work is completed by 8 women in 3/4 day, or 18 children together can finish the same work in 1/2 day. If 3 women and 3 children were employed to work for a day , then how many men for how many days be employed to complete the work ?
a) 1 day
b) 2 days
c) ½ day
d) 2 ½ days
Answer: ( c)
Explanation : 3 men do the work in 1 day
8 women do the work in ¾ day
1 women will do the work in 3/4 * 8 = 6 days
Again, 18 children do the work in ½ day
1 child will do the work in ½ * 18 =9 days
A women does in 6 days = 1 work
1 women will do in 1 day = 1/6 work
3 women will do in 1 day = 1/6 * 3 = ½ work
1 child does in 9 boys = 1 work
1child will do in 1 day = 1/9 work
Work done by ( 3 women + 3 children) in 1 day = ½ + 1/3 = 5/6
Remaining work = 1-5/6 = 1/6
This part of work is to be completed by man.
1 man does 1 work in 3 days
1man will do 1/6 work in = 3/6 = ½ day
So 1 man should be employed for ½ day
Ques 3)
Water is following at the rate of 7metres per second through a circular pipe whose diameter is 2 cm into a cylindrical tank the radius of whose base is 40cm. Determine the increase in water level in ½ hour.
a)595cm
b)587.5
c)878.5cm
d)787.5 cm
Answer: (d)
Explanation: Rate of flow of water = 7m per sec = 700 cm per second
Length of water column in ½ hour = (700 * 30 * 60 )
Internal radius of circular pipe = 1cm
Obviously, water column forms a cylinder of radius 1cm and length = (700*30*60 ) cm
Volume of water that flows in tank in ½ hour = 22/7 * 1 * 1 * 700 * 30 * 60
V= πr2 h
Let h cm be the rise in the level of water in the tank. Then,
Volume of water in the tank = 22/7 * 40 * 40 * h
Both volumes are equal
22/7 * 40 * 40 * h = 22/7 * 1 * 1 * 700 * 30 * 60
H= 787.5 cm ( rise in level )
Ques 4)
In a shop , the prices of all the goods are marked 15% above the cost price and 5% discount is allowed on all sales. In a certain month the business expenses of the shop amounted to Rs. 6500 and the owner realized a profit of 6%. Find the cost price of the goods sold by the shop during the month.
a) 22000
b)200000
c)20000
d)220000
Answer : (b)
Explanation:Let the cost price of the goods sold during the month be Rs. X
Marked price at 15% above cost price = 1.15x
Sale price after 5% discount = 0.95 * 1.15 x = 1.0925 x
Expenses= 6500
Profit during the month = 6% which can be equated as 1.0925 x – 1.06x = 6500
0.0325x = 6500
X= Rs. 200000
Ques 5)
Two bullets were fired at a place at an interval of 12 minutes. A person approaching the firing point in his car hears the two sounds at an interval of 11 minutes 40 seconds. The speed of sound is 330 metres per second. What is the speed of the car?
Answer: (a)
Explanation: If the car were not moving , the person would have heard the sounds at an interval of 12 minutes. Therefore ,the distance travelled by car in 11 minutes 40 seconds is equal to the distance that could have been covered by sound in 12min – 11min.40seconds = 20seconds
Distance covered by sound in 20 seconds = 330*20 = 6600 m
In 11minutes , 40seconds = 700 seconds that the car travels 6600 m
In 1sec the car will travel 6600/700 = 66/ 7 metre per second
Speed of the car = 66/7 * 18/5 km per hour
=1188/35
Speed of the car =
km per hour
