**1.Six years ago, the ratio of the ages of Kunal and Sagar was 6:5, Four years hence, the ratio of their ages will be 11:10. What is Sagar age at present**

a.10 years

b.12 years

c.14 years

d.16 years

**2. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is**

a.20 years

b.21 years

c.22 years

d.24 years

**3. A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:**

a. 3 : 1

b. 1 : 3

c. 1 : 2

d. 2 : 1

**4.Tap ‘A’ can fill the tank completely in 6 hrs while tap ‘B’ can empty it by 12 hrs. By mistake, the person forgot to close the tap ‘B’, As a result, both the taps, remained open. After 4 hrs, the person**

**realized the mistake and immediately closed the tap ‘B’. In how much time now onwards, would the tank be full?**

a. 2 hours

b. 4 hours

c. 5 hours

d. 1 hour

**5.A man can row at a speed of 12 km/hr in still water to a certain upstream point and back to the starting point in a river which flows at 3 km/hr. Find his average speed for total journey.**

a. 12 3/4 km/hr

b. 11 3/4 km/hr

c. 12 1/4 km/hr

d. 11 1/4 km/hr

**6.How many litres of water must be added to 16 liters of milk and water contains 10% water to make it 20% water in it?**

a. 4 litre

b. 2 litre

c. 1 litre

d. 3 litre

**7.John bought 20 kg of wheat at the rate of Rs.8.50 per kg and 35 kg at the rate of Rs.8.75 per kg. He mixed the two. Approximately at what price per kg should he sell the mixture to make 40% profit as the cost price?**

a. Rs.12

b. Rs.8

c. Rs.16

d. Rs.20

**8.Mr. Mani invested an amount of Rs. 12000 at the simple interest rate of 10% per annum and another amount at the simple interest rate of 20% per annum. The total interest earned at the end of one year on the total amount invested became 14% per annum. Find the total amount invested.**

a. Rs. 25000

b. Rs. 15000

c. Rs. 10000

d. Rs. 20000

**9.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?**

a. 3.46%

b. None of these

c. 4.5%

d. 5%

**10. At what rate percent of simple interest will a sum of money double itself in 20 years?**

a. 4%

b. 5%

c. 6%

d. 8%

*Answers:*

**1.D**

**Let six years ago the age of Kunal and Sagar are 6x and 5x resp.**

**then,**

**((6x+6)+4)/((5x+6)+4)=11/10**

**10(6x+10)=11(5x+10)**

**5x=10=>x=2**

**So Sagar age is (5x+6) = 16**

**2.C**

**Let the son’s present age be x years. Then, man’s present age = (x + 24) years**

**(x + 24) + 2 = 2(x + 2)**

**x + 26 = 2x + 4**

**So, x = 22**

**3.A**

**Let speed upstream = x**

**Then, speed downstream = 2x**

**Speed in still water = (2x+x)/2=3x/2**

**Speed of the stream = (2x−x)/2=x/2**

**Speed in still water : Speed of the stream = 3x/2:x/2 = 3 : 1**

**4.B**

**Tap A can fill the tank completely in 6 hours**

**In 1 hour, Tap A can fill 1⁄6 of the tank**

**Tap B can empty the tank completely in 12 hours**

**In 1 hour, Tap B can empty 1⁄12 of the tank**

**i.e., In one hour, Tank A and B together can effectively fill 1⁄6 – 1⁄12 = 1⁄12 of the tank**

**In 4 hours, Tank A and B can effectively fill 1⁄12 × 4 = 1⁄3 of the tank.**

**Time taken to fill the remaining 1−1/3=2/3of the tank =(2/3)/(1/6) = 4 hours**

**5.D**

**Speed of the man in still water = 12 km/hr**

**Speed of the stream = 3 km/hr**

**Speed downstream = (12+3) = 15 km/hr**

**Speed upstream = (12-3) = 9 km/hr**

**Average Speed = (Speed downstream × Speed downstream)/Speed in still water=(15×9)/12=(15×3)/4=45/4=11 1/4 km/hr**

**6.B**

**By the rule of alligation, we have**

**% Concentration of water**

**in pure water : 100 % Concentration of water in the given mixture : 10**

**Mean % concentration**

**20**

**20 – 10 = 10 100 – 20 = 80**

**Quantity of water : Quantity of the mixture = 10 : 80 = 1 : 8**

**Here Quantity of the mixture = 16 litres**

**Quantity of water : 16 = 1 : 8**

**Quantity of water = 16×1/8=2 litre**

**7.A**

**CP=20×8.5+35×8.75=170+306.25=476.25**

**Profit=40%**

**SP=((100+Profit%)/100)×CP=((100+40)/100)×476.25=140/100×476.25=140/4×19.05=35×19.05**

**Total quantity = 20 + 35 = 55 Kg**

**SP per Kg=(35×19.05)/55=(7×19.05)/11≈(7×19)/11≈133/11≈12**

**8.D**

**If an amount P1 is lent out at simple interest of R1% per annum and another amount P2 at simple interest rate of R2% per annum, then the rate of interest for the whole sum can be given by**

**R=(P1R1+P2R2)/P1+P2**

**P1 = Rs. 12000, R1 = 10%**

**P2 = ?, R2 = 20%**

**R = 14%**

**14=(12000×10+P2×20)/12000+P2**

**12000×14+14P2=120000+20P2**

**6P2=14×12000−120000=48000**

**P2=8000**

**Total amount invested = (P1 + P2) = (12000 + 8000) = Rs. 20000**

**9.A**

**Let the sum of Rs.725 is lent out at rate R% for 1 year**

**Then, at the end of 8 months, ad additional sum of 362.50 more is lent out at rate 2R% for remaining 4 months(1/3 year)**

**Total Simple Interest = 33.50**

**[(725×R×1)/100]+[(362.50×2R×1/3)/100]=33.50**

**(725×R×1)/100+(362.50×2R)/300=33.50**

**R=502.5/145=3.46%**

**10.B**

**Let sum = x**

**Time = 20 years**

**Simple Interest = x**

**R = (100×SI)/PT=(100×x)/(x×20)=100/20=5%**