34705.In a covering, a certain distance, the speeds of A and B are in the ratio of 3:4. A takes 30 minutes more than B
to reach the destination. The time taken by A to reach the destination is?
to reach the destination. The time taken by A to reach the destination is?
1 hour
1 1/2 hour
2 hour
2 1/2 hour
Explanation:
Ratio of speeds = 3:4
Ratio of times taken = 4:3
Suppose A takes 4x hrs and B takes 3x hrs to reach the destination.
Then, 4x - 3x = 30/60 $\Rightarrow$ x = 1/2
Time taken by A = 4x hrs = 4 $\times$ 1/2 = 2 hrs.
Ratio of speeds = 3:4
Ratio of times taken = 4:3
Suppose A takes 4x hrs and B takes 3x hrs to reach the destination.
Then, 4x - 3x = 30/60 $\Rightarrow$ x = 1/2
Time taken by A = 4x hrs = 4 $\times$ 1/2 = 2 hrs.
34706.A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr
in the direction opposite to that in which the train is going?
in the direction opposite to that in which the train is going?
5 sec
6 sec
7 sec
10 sec
Explanation:
Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 $\times$ 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 $\times$ 3/55 = 6 sec.
Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 $\times$ 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 $\times$ 3/55 = 6 sec.
34707.A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With
the help of C, they completed the work in 3 days. How much is to be paid to C?
the help of C, they completed the work in 3 days. How much is to be paid to C?
Rs. 375
Rs. 400
Rs. 600
Rs. 800
Explanation:
C`s 1 day`s work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24
A`s wages : B`s wages : C`s wages
1/6 : 1/8 : 1/24 = 4:3:1
C`s share = 1/8 $\times$ 3200 = Rs. 400
C`s 1 day`s work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24
A`s wages : B`s wages : C`s wages
1/6 : 1/8 : 1/24 = 4:3:1
C`s share = 1/8 $\times$ 3200 = Rs. 400
34708.A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?
Rs. 300
Rs. 400
Rs. 500
Rs. 600
Explanation:
Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1500
$\Rightarrow$ 5 parts out of 15 parts is Rs. 1500
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (1500) = Rs. 600
Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1500
$\Rightarrow$ 5 parts out of 15 parts is Rs. 1500
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (1500) = Rs. 600
34709.If Rs. 510 be divided among A, B, C in such a way that A gets 2/3 of what B gets and B gets 1/4 of what C gets,
then their shares are respectively:
then their shares are respectively:
Rs. 120, Rs. 240, Rs. 150
Rs. 60, Rs. 90, Rs. 360
Rs. 150, Rs. 300, Rs. 60
None of these
Explanation:
(A = 2/3 B and B = 1/4 C) = A/B = 2/3 and B/C = 1/4
A:B = 2:3 and B:C = 1:4 = 3:12
A:B:C = 2:3:12
A`s share = 510 $\times$ 2/17 = Rs. 60
B`s share = 510 $\times$ 3/17 = Rs. 90
C`s share = 510 $\times$ 12/17 = Rs. 360.
(A = 2/3 B and B = 1/4 C) = A/B = 2/3 and B/C = 1/4
A:B = 2:3 and B:C = 1:4 = 3:12
A:B:C = 2:3:12
A`s share = 510 $\times$ 2/17 = Rs. 60
B`s share = 510 $\times$ 3/17 = Rs. 90
C`s share = 510 $\times$ 12/17 = Rs. 360.
34710.The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours,then find the speed of the boat in still water?
10 kmph
21 kmph
8 kmph
12 kmph
Explanation:
S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
34711.In how much time would the simple interest on a certain sum be 0.125 times the principal at 10% per annum?
1 1/4 years
1 3/4 years
2 1/4 years
2 3/4 years
Explanation:
Let sum = x. Then, S.I. = 0.125x = 1/8 x, R = 10%
Time = (100 $\times$ x) / (x $\times$ 8 $\times$ 10) = 5/4 = 1 1/4 years.
Let sum = x. Then, S.I. = 0.125x = 1/8 x, R = 10%
Time = (100 $\times$ x) / (x $\times$ 8 $\times$ 10) = 5/4 = 1 1/4 years.
34712.Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?
Rs.150
Rs.132
Rs.100
Rs.125
Explanation:
2 $\times$ 22/7 $\times$ 14 = 88
88 $\times$ 1 1/2 = Rs.132
2 $\times$ 22/7 $\times$ 14 = 88
88 $\times$ 1 1/2 = Rs.132
34713.A pupil`s marks were wrongly entered as 83 instead of 63. Due to the average marks for the class got increased by half. The number of pupils in the class is:
10
20
40
73
Explanation:
Let there be x pupils in the class.
Total increase in marks = (x $\times$ 1/2) = x/2
x/2 = (83 - 63) $\Rightarrow$ x/2 = 20 $\Rightarrow$ x = 40.
Let there be x pupils in the class.
Total increase in marks = (x $\times$ 1/2) = x/2
x/2 = (83 - 63) $\Rightarrow$ x/2 = 20 $\Rightarrow$ x = 40.
34714.The H.C.F of two numbers is 11 and their L.C.M is 7700. If one of the numbers is 275, then the other is:
279
283
308
318
Explanation:
Other number = (11 $\times$ 7700)/275 = 308.
Other number = (11 $\times$ 7700)/275 = 308.
34715.If the sum of the two numbers is 22 and the sum of their squares is 404, then the product of the numbers is:
40
44
80
88
Explanation:
Let the numbers be x and y.
Then, (x + y) = 22 and x2 + y2 = 404
Now,
2xy = (x + y)2 - (x2 + y2)
2xy= 222 - 404 = 484 - 404 = 80
xy = 40
Let the numbers be x and y.
Then, (x + y) = 22 and x2 + y2 = 404
Now,
2xy = (x + y)2 - (x2 + y2)
2xy= 222 - 404 = 484 - 404 = 80
xy = 40
34716.Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively.When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?
5/11
6/11
7/11
8/11
Explanation:
Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10) = 11/20
Part filled by C in 3 minutes = 3/10
Required ratio = 3/10 $\times$ 20/11 = 6/11
Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10) = 11/20
Part filled by C in 3 minutes = 3/10
Required ratio = 3/10 $\times$ 20/11 = 6/11
34717.The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?
Rs. 3096
Rs. 4076
Rs. 4085
Rs. 4096
Explanation:
Principal = [4913 / (1 + 25/(4 $\times$ 100))3]
= 4913 $\times$ 16/17 $\times$ 16/17 $\times$ 16/17 = Rs. 4096.
Principal = [4913 / (1 + 25/(4 $\times$ 100))3]
= 4913 $\times$ 16/17 $\times$ 16/17 $\times$ 16/17 = Rs. 4096.
34718.If the height of a cone is increased by 100% then its volume is increased by?
100%
200%
300%
400%
34719.Find the one which does not belong to that group?
Walk
Talk
Drink
Plank
Explanation:
Walk, Talk, Drink and Lick are verbs, but not Plank.
Walk, Talk, Drink and Lick are verbs, but not Plank.
34720.A sells a bicycle to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays Rs. 225 for it, the cost price of the bicycle for A is:
Rs. 110
Rs. 120
Rs. 125
Rs. 150
Explanation:
125% of 120% of A = 225
125/100 $\times$ 120/100 $\times$ A = 225
A = 225 $\times$ 2/3 = 150.
125% of 120% of A = 225
125/100 $\times$ 120/100 $\times$ A = 225
A = 225 $\times$ 2/3 = 150.
34721.A person`s present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old id the mother at present?
32 years
36 years
40 years
48 years
Explanation:
Let the mother`s present age be x years. Then, the person`s present age = 2/5 x years.
(2/5 x + 8) = 1/2 (x + 8)
2(2x + 40) = 5(x + 8) $\Rightarrow$ x = 40
Let the mother`s present age be x years. Then, the person`s present age = 2/5 x years.
(2/5 x + 8) = 1/2 (x + 8)
2(2x + 40) = 5(x + 8) $\Rightarrow$ x = 40
34722.In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 8720 votes were polled, then how many valid votes did B get?
2160
2420
2834
3150
Explanation:
Let the total number of votes polled in the election be 100k.
Number of valid votes = 100k - 20% (100k) = 80k
Let the number of votes polled in favour of A and B be a and b respectively.
a - b = 15% (100k) $\Rightarrow$ a = b + 15k
$\Rightarrow$ a + b = b + 15k + b
Now, 2b + 15k = 80k and hence b = 32.5k
It is given that 100k = 8720
32.5k = 32.5k/100k $\times$ 8720 = 2834
The number of valid votes polled in favour of B is 2834.
Let the total number of votes polled in the election be 100k.
Number of valid votes = 100k - 20% (100k) = 80k
Let the number of votes polled in favour of A and B be a and b respectively.
a - b = 15% (100k) $\Rightarrow$ a = b + 15k
$\Rightarrow$ a + b = b + 15k + b
Now, 2b + 15k = 80k and hence b = 32.5k
It is given that 100k = 8720
32.5k = 32.5k/100k $\times$ 8720 = 2834
The number of valid votes polled in favour of B is 2834.
34723.The cost of 16 pens and 8 pencils is Rs.352 and the cost of 4 pens and 4 pencils is Rs.96. Find the cost of each
pen?
pen?
Rs.32
Rs.28
Rs.36
None of these
Explanation:
Let the cost of each pen and pencil be `p` and `q` respectively.
16p + 8q = 352 --- (1)
4p + 4q = 96
8p + 8q = 192 --- (2)
(1) - (2) $\Rightarrow$ 8p = 160
$\Rightarrow$ p = 20
Let the cost of each pen and pencil be `p` and `q` respectively.
16p + 8q = 352 --- (1)
4p + 4q = 96
8p + 8q = 192 --- (2)
(1) - (2) $\Rightarrow$ 8p = 160
$\Rightarrow$ p = 20
34724.I. a2 + 11a + 30 = 0,
II. b2 + 6b + 5 = 0 to solve both the equations to find the values of a and b?
II. b2 + 6b + 5 = 0 to solve both the equations to find the values of a and b?
If a < b
If a = b
If the relationship between a and b cannot be established
If a > b
Explanation:
I. (a + 6)(a + 5) = 0
$\Rightarrow$ a = -6, -5
II. (b + 5)(b + 1) = 0
$\Rightarrow$ b = -5, -1 $\Rightarrow$ a = b
I. (a + 6)(a + 5) = 0
$\Rightarrow$ a = -6, -5
II. (b + 5)(b + 1) = 0
$\Rightarrow$ b = -5, -1 $\Rightarrow$ a = b