1. A and B started a business making an initial investment of Rs 15000 and Rs 24000 respectively. At the end of the year A got a total amount (amount invested + Profit before tax) of Rs 20000. If they have to pay income tax on the total profit @ 10% then how much tax they have paid?

Ans:1
Ratio in which Profit will be divided between Jai and Vijay =15000: 24000 = 5: 8
Total profit that obtained by A at the end of the year = Rs (20000 – 15000) = Rs 5000
Hence total profit that both A and B obtained at the end of the year = Rs 5000/5 X 13 = Rs 13000
Therefore, total tax paid by A and B at the end of the year = Rs (13000 X 0.1) = Rs 1300

 

2. Riya’s expenditure and savings are in the ratio of 5:3. If the income increases by 16% and expenditure increases by 10%, find the effect on savings :

Ans:1
Let expenditure = 50 and savings = 30
=> Therefore income =50+30=80
=> Now increase in income = 16%
=> Therefore new income = 16*80/100 + 80 = 464/5
=> Increase in expenditure = 10%
=> Therefore new expenditure = 10*50/100 + 50 = 55
=> Therefore savings = 464/5 – 55 = 189/5
=> Increase in savings = 189/5 -30 = 39/5
=> Percentage increase = 39*100/(5*30) = 26%

 

3. A dealer increased the original selling price of the item by 10% and later he decreased it by 10% and thus sold that item at Rs 1188. What was the original selling price of the item?

Ans:4
Let the original selling price of the item be Rs 100n
Selling price after increasing it by 10% = Rs (100n X 1.1) = Rs 110n
Selling price after decreasing it by 10% = Rs (110n X 0.9) = Rs 99n
According to the question, 99n = 1188
=> n = 12
Hence original selling price of the item = Rs (100 X 12) = Rs 1200

 

4. A man borrows a certain sum of money and pays it back in 2 yrs in two equal installments. If C.I. is reckoned at 5% per annum and he pays back annually Rs. 441, what sum did he borrow?

Ans:1
Money borrowed that becomes 441 in 1 year = 441 / (1 + 5/100) = 441 x 20 /21 = 420

Money borrowed that becomes 441 in 2 years = 441 / (1 + 5/100)2 = 441 x (20/21) x (20/21) = 400

Total Money = 420 + 400 = 820

 

5. A train travels for 40 km/h but after travelling every 45 minutes it stops for 10 minutes. After exactly 6 hours what will be the average velocity of the train?

Ans:3
In 45 minutes it travels = 45/60 x 40 = 30 km
Now it takes a rest of 10 minutes so actually in 55 minutes it travels 30 km.
So by this we can say it will travel 30 x 6 = 180 km in 55 x 6 = 330 minutes.
So in 6 hours we are left with another 30 minutes. In 30 minutes it travels 30/60 x 40 = 20 km.
It travels a total of 180 + 20 = 200 km.
So the average velocity = 200/ 6 = 33 1/3

 

6. Ram can row downstream 18 kms in 4 hours and the same distance upstream in 12 hours. Find the speed of rowing of Ram in still water(in km/hr)?

Ans:1
Let x = speed of rowing of Ram in still water; y = speed of stream
x + y = 18/4 => x + y = 4.5 — (1)
And x – y = 18 => x + y = 1.5 — (2)
Solving (1) and (2), we get
x = 3; y = 1.5
Speed of Ram = 3 km/hr

 

7. 50 people can complete a work in 20 days. A contractor has employed 35 people to complete the work. However after 12 days he gets a notice that he has to complete the remaining work within 3 days. Then how many more people does he have to employ to finish the work on time?

Ans:2
Total work = 50 x 20 = 1000 units of man days
Work done by 12 people in 35 days = 35 x 12 = 420 man days
Remaining work = 1000 – 420 = 580 man days
Let the number of people to be added be N.
Therefore, (N+35) x 3 = 580
N+35 = 580/3
N+35 = 193.33 = 194 people (people have to be an integral number)
Or N = 159 people

 

8. The average weight of 8 persons increases by 2.5 kg when a new person comes in place of a person of weight 65 kg. What is the weight of the new person?

Ans:2
Let the initial average be A.
Then total weight of the 8 persons is 8A.
When a person of weight 65 kg is replaced by another person of weight w, the average increases by 2.5.
Therefore A+2.5 = (8A-65 + w)/8
=> 8A + 20 = 8A – 65 + w
=> w = 85

 

9. A mixture which contains milk and 60 liters of water costs Rs 10 per liter. If the price of the pure milk is Rs 15 per liter then what is the total volume of mixture?

Ans:5
According to the question price of 1 liter of the pure milk is = Rs 15

Hence amount of milk in the mixture when cost of 1 liter of the mixture is Rs 10 = 10/15=2/3 liter

It means 1/3th part of the mixture is water and 2/3rd part of the mixture is pure milk.

Hence total quantity of the milk = 60 X 2 = 120 liters

Therefore total volume of the mixture = 120 + 60 = 180 liter

 

10. Pankaj and Kumar started a business with an initial investment in the ratio of 7 : 8. After 8 months Pankaj adds Rs.75 more to his capital while Kumar withdraws Rs.200 from his capital. At the end of the year the profit is distributed between them in the ratio 15 : 16. What is the difference between initial investment of Pankaj and Kumar?

Ans:4
Let initial investment of Pankaj and Kumar is ‘7x’ and ‘8x’ respectively.
Ratio of their profit at the end of the year = [7x * 8 + (7x + 75) * 4] : [8x * 8 + (8x – 200) * 4] = 15 : 16
=> (84x + 300) : (96x – 800) = 15 : 16
=> 16(84x + 300) = 15(96x – 800)
=> 1440x – 1344x = 4800 + 12000
=> 96x = 16800
=> x = 175
Required difference = 8x – 7x = x = Rs.175

 

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