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1. One type of rice having price of Rs 12/kg is mixed with another type of rice in the ratio of 8:7. Find the price of second type if the mixture is worth Rs 10 per kg.

2. A man has placed oil in 7 bottles of equal size. He is selling oil at the rate of Rs 5 per liter and is losing Rs 200 in the whole transaction. If he starts selling at Rs 6 per liter, he will gain Rs 150 on the whole. Find the capacity of each bottle. (Consider the oil is filled in the bottle with 100% of its capacity)

3. A, B and C started a business by investing in the ratio of 9: 4: 6 respectively. A manages the business and for this activity he gets an amount of Rs 30,000 at the end of the year. If at the end of the year total profit obtained by them are in the ratio of 6: 2: 3 then what is the profit C got at the end of the year?

4. If the price of oil increases by 25%, by what percentage should the consumption be reduced so that the expenditure on oil can be the same?

5. A sum of money lent at compound interest for 1 year at 40% per annum compounded annually would fetch Rupees 8333 more, if the interest was payable quarterly, then sum of money is

6. Two trains running in opposite directions cross each other in 25 seconds. The lengths of the first train and second train are 429m and 346m respectively. Also, the speed of the 1^{st} train is 72kmph. Find the speed of the second train.

7. A can fill a tank in 30 mins and B takes 48 min to fill the tank. C can empty the tank in 60 min. Find the time taken to fill the tank if all three pipes are opened simultaneously.

8. Pure ghee cost Rs. 800 per litre. A shopkeeper adds refined ghee in-to 30 litre of pure ghee and sells the mixture at Rs. 600 per litre. How many liters of refined ghee does he added? [Assume the cost of refined ghee to be zero and after selling there will be no profit and no loss.]

9. The average age of 24 worker of a factory is 28 years. The average age of factory becomes 28.24 when a new person joins the factory. The average age of factory again becomes 28 when another person joins the factory. Find the difference between ages of both the new joinee.

10. The sum of the circumference of a circle and the perimeter of a square is equal to 256 cm. The diameter of the circle is 56 cm. What is the sum of the areas of the circle and the square?

**Check your Answers below:**

##### 1. Question

One type of rice having price of Rs 12/kg is mixed with another type of rice in the ratio of 8:7. Find the price of second type if the mixture is worth Rs 10 per kg.

Ans:3

Let the price of second type be y.=> (12-10) / (10-y) = 7/8

=> 16 = 70-7y

=> 7y = 54

=> y = 54/7

=> Rs 7.71 /kg

##### 2. Question

A man has placed oil in 7 bottles of equal size. He is selling oil at the rate of Rs 5 per liter and is losing Rs 200 in the whole transaction. If he starts selling at Rs 6 per liter, he will gain Rs 150 on the whole. Find the capacity of each bottle. (Consider the oil is filled in the bottle with 100% of its capacity)

Ans:1

Let the total oil be x liters.

5x + 200 = Cost price of oil

Also 6x – 150 = Cost price of oil

5x + 200 = 6x – 150

x = 350

Qty in each bottle = 350/7

=> 50 lit##### 3. Question

A, B and C started a business by investing in the ratio of 9: 4: 6 respectively. A manages the business and for this activity he gets an amount of Rs 30,000 at the end of the year. If at the end of the year total profit obtained by them are in the ratio of 6: 2: 3 then what is the profit C got at the end of the year?

Ans:4

According to the question profit obtained by A, B and C at the end of the year will be Rs (9n + 30000), Rs 4n and Rs 6n respectively.

Therefore, total profit obtained at the end of the year = Rs (9n + 4n + 6n + 30000) = Rs (19n + 30000)

According to the question; (9n+30000)/4n=6/2

=> (9n + 30000) = 12n

=> 3n = 30000

=>n = 10000

Therefore, total profit obtained by C at the end of the year = Rs 6n = Rs 60000##### 4. Question

If the price of oil increases by 25%, by what percentage should the consumption be reduced so that the expenditure on oil can be the same?

Ans:1

Let initial price be P.

Let consumption be C.

Let consumption after decrease be “C x R”.

1.25P x C x R = P x C

R = 1/1.25 = 0.8

So the decrease = C – 0.8C = 0.2C which is 20%.##### 5. Question

A sum of money lent at compound interest for 1 year at 40% per annum compounded annually would fetch Rupees 8333 more, if the interest was payable quarterly, then sum of money is

Ans:1

Let the sum be P.

CI at annual compounding = P(1+R/100) – P

= P(1 + 40/100) – P = 0.4 P

CI at quarterly compounding = P(1+R/400)4 – P

= P(1 + 1/10)4 – P = 0.4641 P

Difference in interest = 0.0641 P = 8333

=> P = Rs 130000##### 6. Question

Two trains running in opposite directions cross each other in 25 seconds. The lengths of the first train and second train are 429m and 346m respectively. Also, the speed of the 1

^{st}train is 72kmph. Find the speed of the second train.Ans:2

Speed of the 1^{st}train=72kmph=72*5/18=20m/sLet the speed of the second train be X m/s.

Time=sum of length of the two trains/sum of their speeds

25=(429+346)/(20+X)

(20+X)=775/25=31

X=31-20=11m/s

Hence, the speed of the second train=11m/s

##### 7. Question

A can fill a tank in 30 mins and B takes 48 min to fill the tank. C can empty the tank in 60 min. Find the time taken to fill the tank if all three pipes are opened simultaneously.

Ans:3

=> Tank filled by A in 1 min = 1/30

=> Tank filled by B in 1 min = 1/48

=> Tank filled by C in 1 min = 1/60

When all pipes are opened together, tank filled in one minute = 1/30 + 1/48 – 1/60

= 9/240

Total time = 240/9 min = 240/(9*60) hrs = 4/9 hrs.##### 8. Question

Pure ghee cost Rs. 800 per litre. A shopkeeper adds refined ghee in-to 30 litre of pure ghee and sells the mixture at Rs. 600 per litre. How many liters of refined ghee does he added? [Assume the cost of refined ghee to be zero and after selling there will be no profit and no loss.]

Ans:1

Cost of 30 litre pure ghee = Rs 24000

Now he sells mixture at Rs 600

Since, he sells at no profit-no loss. So, total selling price accumulated after selling the mixture is = 24000

Therefore, total quantity of ghee sold = 24000/600 = 40 litre

So, 10 litre of refined has been added in the pure ghee.##### 9. Question

The average age of 24 worker of a factory is 28 years. The average age of factory becomes 28.24 when a new person joins the factory. The average age of factory again becomes 28 when another person joins the factory. Find the difference between ages of both the new joinee.

Ans:3

Total age of 24 workers = 24 * 28 = 672

Total age of 25 worker = 25 * 28.24 = 706

Age of first joinee = 706 – 672 = 34 year

Total age of 26 workers = 26 * 28 = 728

Age of the second joinee = 728 – 706 = 22 year

Required difference = 34 – 22 = 12 years##### 10. Question

The sum of the circumference of a circle and the perimeter of a square is equal to 256 cm. The diameter of the circle is 56 cm. What is the sum of the areas of the circle and the square?

Ans:3

Circumference of circle = 56 x 22/7 = 176

Perimeter of square = 256 – 176 = 80

Hence side = 20

Required sum of area = 22/7 x 28 x 28 + 20 x 20

2464+400 = 2864