1. The average marks scored by Gattu in English, Science, Mathematics and History is 12 less than the average marks scored by him in English, History, Geography and Mathematics. What is the difference in marks scored by him in Science and Geography?

Ans:5
Let the marks scored in English, Science, Mathematics, History and Geography be E, S, M, H and G respectively.
Average marks scored= (Total marks scored in given subjects)/(number of subjects)
According to question,(E+H+G+M)/4- (E+S+M+H)/4=12
=>G – S = 48

 

2. A boy is riding a bicycle on a circular track and wants to cover a distance of 5.28km. If the radius of circular track is 84m. Then in how many rounds will the boy be able to cover the required distance?

Ans:4
Circumference of circular track = 2πr
On solving, circumference = 528m
Therefore, number of rounds to cover the distance = 5280m/528m = 10

 

3. Raman and Raghav enter into a partnership with initial investment Ra.3500 and Ra.5000 respectively. At the end of 2 years Raghav left the business and Puneet joined Raman with the initial investment of Rs.4500. If at the end of 5 years difference between profit share of Raghav and Puneet is Rs.2800, then find the share of Raman in the business.

Ans:3
Ratio of share of profit at the end of 5 years = (3500 * 5) : (5000 * 2) : (4500 * 3) = 35 : 20 : 27
Let total profit = 100P
Difference between profit share of Raghav and Puneet = 100P * (27 – 20)/(35 + 20 + 27) = 2800
=> 700P/82 = 2800
=> P = 328
Share of Raman = 100P * (35/82) = 32800 * (35/82) = Rs.14000

 

4. Kiran spent Rs 5475 on her parties, Rs 8525 on shopping from his monthly income and then she saved 36% of her monthly salary. What was her annual income?

Ans:1
Let the monthly income of Kiran= Rs x
(100 – 36) % of x= (5475 + 8525)
64% of x = 14000
x = (14000 * 100)/ 64 = 21875
So, annual income= 21875 * 12 = Rs 262500

 

5. A cricket ball is sold at Rs 400 and the seller realized a loss of n%. If the seller would have sold the ball at Rs 500 then he would have realized a profit of 2n%. What is the value of n?

Ans:5
Let the cost price of the ball be Rs A

Hence, A (1 – n/100) = 400… (1)

According to the 2nd condition, A(1 + 2n/100) = 500…(2)

From (1) and (2) we get,

=> 5(1 – n/100) = 4(1 + 2n/100)

=> 5 – 5n/100 = 4 + 8n/100

=> 13n/(100)=1

=> n = 100/13=7.7%

 

6. A mixture of milk and water contains 20% water. What quantity of pure milk should be added to 500 liters of this mixture to reduce water to 5%?

Ans:4
Total amount of water in 500 liter mixture = (500 X 0.2) liter = 100 liter
Let’s assume total amount of milk added = M liter
Hence; 100/((500+M))=5/100
=> 500 + M = 2000
=> M = 1500

 

7. Arun covers a total distance of 500 km by Bus, Train and Bike in the ratio of 3 : 4 : 2 respectively. The speeds of Bus, Bike and Train are in the the ratio of 3 : 2 : 4. If the total duration of the journey was 25 hours then find out the ratio of the time taken by Bus, Train and Bike to cover the distance?

Ans:5
Distance on bus, train, bike be 3a,4a,2a respectively.
Speeds of the bus, bike, train be 3b, 2b, 4b respectively.
Time on bus = 3a/3b = a/b
Time on bike = 2a/2b = a/b
Time on train = 4a/4b = a/b
So required ratio = 1:1:1
Note: The speeds mentioned are in the order Bus, Bike and Train, while distance is in the order Bus, Train and Bike.

 

8. Siddhartha took loan from a bank at the rate of 8% p.a. simple interest to start a new business. After 4 years he paid Rs. 3840 interest for this period. The principal amount borrowed by him was:

Ans:3
Given, time (T) = 4 years and simple interest (SI) = Rs. 3840
and rate of interest (r) = 8%
Then, principal (P) = 100 x SI/(rT) = 100 x 3840/(8 x 4) = Rs.12000.
Hence, option 3.

 

9. A train travelling at 42 km/hr passes a cyclist going in the same direction in 9 seconds. If the cyclist had been going in the opposite direction, the train would have passed him in 5 seconds. Find the length of the train.

Ans:1
Let the speed of the cyclist be s km/hr and length of the train be l meter.
When going in same direction, L = (42-s) x 9 x 5/18 (i)
When going in opposite direction, L = (42+s) x 5 x 5/18 (ii)
From eqn (i) and (ii),
378 – 9s = 210 + 5s
=> 14s = 168
Or s = 12 km/h
Putting this value in eqn (i),
L = 30 x 9 x 5/18 = 75m

 

10. Pipe A and B running together can fill a cistern in 6 minutes. If B takes 5 minutes more than A to fill the cistern then the times in which A and B will fill the cistern separately will be, respectively:

Ans:2
suppose A takes x minutes and B takes x+5 minutes
acc to the question, 1/x + 1/(x+5) = 1/6
after solving, x = 10minutes
so A takes 10 minutes and B takes 15 minutes

 

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