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.

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. 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. 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. 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. 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. 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 1st train is 72kmph. Find the speed of the second train.

Ans:2
Speed of the 1st train=72kmph=72*5/18=20m/s

Let 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. 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. 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. 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. 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

 

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