**1. Lucia is a wonderful grandmother. Her age is between 50 and 70.Each of her sons have as many sons as they have brothers. Their combined number gives Lucias age. What is the age?**

a) 60

b) 65

c) 64

d) 66

Explanation:

Let the no. of Lucias sons = n

No. of brothers for each son = n-1

No. of sons for each of Lucias son = n-1

Lucias age = n-1 * n-1

= a perfect square between 50 and 70

= 64

** 2. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:**

a) 1 : 3

b) 3 : 2

c) 3 : 4

d) None of these

**3. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?**

a) 240 m

b) 120 m

c) 300 m

d) None of these

**4. A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is:**

a) 1/4

b) 1/10

c) 7/15

d) 8/15

**5. On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:**

a) Rs. 45

b) Rs. 50

c) Rs. 55

d) Rs. 60

**6. Grass in lawn grows equally thick and in a uniform rate.It takes 40 days for 40 cows and 60 days for 30 cows to eat the whole of the grass.How many days does it take for 20 cows to do the same?**

a) 125

b) 110

c) 120

d) 130

Explanation:

g – grass at the beginning

r – rate at which grass grows, per day

y – rate at which one cow eats grass, per day

n – no of cows to eat the grass in 96 days

g + 40*r = 40 * 40 * y——- 1

g + 60*r = 30 * 60 * y——- 2

g + n*r = 20 * n * y——– 3

from 1 and 2

r=10y g=120r

from 3

nr=120r

Solving, n = 120

**7. When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?**

a) Rs. 21,000

b) Rs. 22,500

c) Rs. 25,300

d) Rs. 25,800

**8. A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?**

a) 12 days

b) 15 days

c) 16 days

d) 18 days