1.

How many seconds will a 500 meter long train moving with a speed of 63 km/hr, take to cross a man walking with a speed of 3 of 3 km/hr is the direction of the train?

**Answer: Option 'B'**

**Distance = 500m
Speed = 63 - 3 km/hr = 60 km/hr
= 600/36 m/s = 50/3 m/s
Time taken = distance/speed = 500/(50/3) = 30 sec**

2.

A cylinder of radius 5m and height 7m is melted to form 11 equal cuboids. Find the volume of the cuboid.

**Answer: Option 'C'**

**Volume of the cylinder = Πr ^{3}h = 550^{3}**

Volume of the cuboid = volume of the cylinder/no of cuboid formed = 550/11 = 50 m^{3}

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3.

If a boat goes 7 km upstream in 42 minuters and the speed of the stream is 3 kmph, then the speed of the boat in still water is

**Answer: Option 'C'**

**Speed Upstream = 7/42 km/min = 7/42 × 60 km/hr
i.e, b = 10 km/hr
speed of the stream = 3 km/hr
Let speed in sttil water is x km/hr
Then, speed upstreeam = (x - 3) km/hr
x - 3 = 10 or x = 13 km/hr**

4.

Raghava buys apples at 3 per kg for Rs. 21 and sells them at 5 kg for Rs. 50. To earn Rs. 102 as profit, he must sell?

**Answer: Option 'B'**

**CP of 1 kg of orange = 21/3 = Rs. 7
SP of 1kg of orange = 50/5 = Rs. 10
Profit in 1kg of orange = Rs. 3
To earn Rs. 102 as profit he must sell 102/3 = 34kg**

5.

4 buses runs between Bhopal and Gwalior. If a man goes from Gwalior to Bhopal by a bus and comes back to Gwalior by another bus, then the total possible ways are

**Answer: Option 'B'**

**Since the man can go in 4 ways and can back in 3 ways.
Therefore total number of ways are 12 ways**

6.

A shopkeeper sells 1 kg of apples for Rs. 160 at a loss of 20%. At what price should he sell a kg of apples to gain 20%?

**Answer: Option 'D'**

**Let the cost price be Rs. (160 + x) Loss = Rs. x Loss% = (x/160+x)) × 100 = 20%
x = Rs. 40
Cost Price = Rs. 200 Gain% = (Gain/ Cost Price) × 100 = 20% Gain = Rs. 40
Selling Price = Gain + Cost Price = Rs. 240/-**

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7.

A, B and C invest in a business. B invests Rs. 5000 more than A and C invests Rs. 5000 more than B. 4/9th of the total profit goes to C. Find the total capital invested in the business.

**Answer: Option 'D'**

**Let the amount of money invested by A be Rs. X
A : B : C = x : x+5000 : x+10000
C's share = (x + 10000)/(3x+15000) = 4/9
Solving the equation,
x = Rs. 10000/-
3x + 15000 = Rs. 45000/-**

8.

Reena scores 80 marks in her first internal maths paper. By how much should she improve her mark in the second internal in order to get an average of 90 in maths?

**Answer: Option 'C'**

**If her average should be 90,
she should score 100 in the second internal.
% improvement = [(100 - 80)/80] × 100 = 25%**

9.

Vamsi started a company investing Rs. 200000. After 8 months, Krishna joined him with a capital of Rs. 120000. After 2 years, they earned a profit of Rs. 42000, what is Krishna's share of the profit?

**Answer: Option 'C'**

**Profits of Vamsi and Krishna are in the ratio 200000 × 24 : 120000 × 16 = 5 : 2
Krishna's share = (2/7) × 42000 = Rs. 12000/-**

10.

A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?

**Answer: Option 'C'**

**Let the original rate be R%. Then, new rate = (2R)%
Note : Here, Original rate is for 1 year(s), the new rate is for only 4 months
that is 1/3 years
[(725 × r × 1)/100] + [(362.50 × 2r × 1)/(100 × 3)] = 33.50
R = 3.46%**

11.

4 singers, 5 dancers and 3 computers divide an amount of Rs. 130000 among themselves such that 3 comperes get as much as 2 dancers and 3 dancers get as much as 2 singers. Find the amount received by singer.

**Answer: Option 'D'**

**4S + 5D + 3C = 130000
3C = 2D
2D = 2S
S = 3D/2 = [4 * (3D/2)] + 5D + 2D = 130000
6D + 5D + 2D = 130000
13D = 130000
D = Rs. 10000
S = 3D/2 = Rs. 15000/-**

12.

Charan is an much younger than Raju as he is older than Tharun. If the sum of the ages of Raju and Tharun is 50 years, what is definitely the difference between Raju and Charan's age?

**Answer: Option 'D'**

**Given that
1. The difference of age between Raju and Charan = The difference of age between Charan and Tharun.
2. Sum of age of Raju and Tharun is 50 i.e (Raju + Tharun) = 50
Question : Raju - Charan = ?
Solution :
Raju - Charan = Charan - Tharun
(Raju + Tharun) = 2Charan
Now given that, (Raju + Tharun) = 50
So, 50 = 2Charan and therefore Charan = 25.
The question is (Raju - Charan) = ?
Here we know the value (age) of Charan(25), but we don't know the age of Raju.
Therefore, (Raju - Charan) cannot be determined**

13.

Pipe A and Pipe B can fill a tank in 20 minutes and 30 minutes respectively. Pipe C can empty the tank in 60 minutes. The tank is initially empty. Both the pipes A and B are opened. Pipe C is opened after 6 minutes. How much time does it take to fill the tank?

**Answer: Option 'D'**

**1/20th of the tank is filled by Pipe A in 1 minute.
1/30th of the tank is filled by Pipe B in 1 minute.
1/60th of the tank is emptied by Pipe C in 1 minute.
Part of tank filled in the first 6 minuters = 6 × [(1/20) + (1/30)] = 1/2 When all pipes are opened,
part of tank filled in 1 minute = (1/12) - (1/60) = 1/15
Time required to fill the remaining 1/2 of the tank = (1/2)/(1/15) = 7.5
Total time = 6 + 7.5 = 13.5 minutes**

14.

A and B are two alloys of gold and copper prepared by mixing metals in the ratio 7 : 2 and 7 : 11 respectively. If equal quantities of the alloys are melted to from a third alloy C, the ratio of gold and copper in C will be?

**Answer: Option 'B'**

**Let 1 kg of each one of A and B be taken to from 2 kg of C.
Gold in 1 kg of A = 7/9, copper in 1 kg of A = 2/9
Gold in 1 kg of B = 7/18, copper in 1 kg og B = 11/18
Gold in 2 kg of C = (7/9 + 7/18) = 21/18 = 7/6
Copper in 2 kg of C = (2/9 + 11/18) = 15/18 = 5/6
Ratio of gold and copper in C = 7/6 : 5/6 = 7 : 5
**

15.

A man bought a television and a DVD player. If he sold the television at a loss of 5% and the player at a gain of 10%, he neither gains nor loses from the transaction. But, if he sells the television at a gain of 20% and the player at a loss of 10% he gains Rs. 3000. Fine the cost price of the television.

**Answer: Option 'B'**

**Let the cost of the television be Rs. x and the player be Rs. y
Case 1 : Loss on selling TV = Gain on selling player
(5/100)x = (10/100)y
0.05x = 0.1y ----(i)
Case 2: Gain selling TV-Loss on selling player = Rs. 3000
(20/100)x - (10/100)y = 3000
0.2x - 0.1y = 3000 --(ii)
Solving (i) and (ii)
x = Rs. 20000/-**

16.

Two trains travelling in opposite directions at speeds of 100 kmph and 90 kmph cross each other for 9s. If the length of the first train is 225m, find the length of the second train.

**Answer: Option 'C'**

**Relative speed of the trains = 110 + 90 = 200 kmph = 200 × 5/18 m/s 200×5/18 = (225+I)/9 I = 275 m**

17.

Pipe A and Pipe B can fill a tank in 1 hour and 1 ¼ hours respectively. Both pipes are opened in the beginning and after some time, pipe B is closed. The tank is filled in 40 minutes. Pipes B was closed after

**Answer: Option 'D'**

**Part of tank filled by A in a minute = 1/60
Part of tank filled by B in a minute = 1/75
Let pipe B be closed after x minutes.
Part of tank filled in x minutes = x * [(1/60)] + (1/75)] =9x/300
Part of tank filled in (40-x) minutes = [(40-x) * (1/60)]
= (40-x)/60
(9x/300) + ((40-x)/60) = 1
4x = 100
x = 25 minutes**

18.

Raj lends a sum of money to Shyam at an interest rate of 5% p.a. After two years, he charges an interst of 8% p.a. At the end of five years, Shyam pays Rs. 13400/- to Raj, how much money did he initially borrow?

**Answer: Option 'B'**

**Let the sum of money be Rs. x
Total Interest = (x × 2 × 5/100) + (x × 3 × 8/100) = 0.34x
x + 0.34x = 1.34x = 13400
**

19.

Excluding stoppages, the average speed of a buss is 54 km/hr and including stoppages, it is 45 km/hr. For how many minutes does the bus stop per hour?

**Answer: Option 'C'**

**Due to stoppages, the bus travels only 45 kms in an hour (9 kms less). To cover a distance of 9 km at a speed of 54 kmph, time taken = 9/54 = 1/6 hrs = 10 mins.**

20.

A jar contains 10 liters of milk. After selling 1 liter of milk, the milkman adds 1 liter of water to the jar. He repeats the process again. What is the percentage of milk contained in the jar now?

**Answer: Option 'C'**

**Amount of milk after 2 operations
= 10[1 - (1/10)] ^{2}
= 10 × (9/10) × (9/10)
= 8.1 litres
% of milk = (8.1/10)×100 = 81%**

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