**1).**

**Five years ago, Somu’s age was 1/3 of Arjun’s age at that time. The ratio of Arjun’s age six years hence to Somu’s age twelve years hence will be 7 : 4. What was Somu’s age three years ago? (in years)**

a) 13

b) 29

c) 17

d) 25

e) 27

**2).**

**A bag contains 24 eggs, out of which 8 are rotten. The remaining eggs are not rotten. Two eggs are selected at random. What is the probability that one of the eggs is rotten?**

a) 11/23

b) 17/23

c) 13/23

d) 32/69

e) 62/69

**3).**

**Akbar, Babu and Charles started a business with their investment in the ratio of 1 : 3 : 5. After 4 months, Akbar invested the same amount as before but Babu as well as Charles withdrew half of their investments. The ratio of their profits at the end of the year is**

a) 1 : 2 : 3

b) 3 :4 :15

c) 3 : 5 : 10

d) 5:6:10

e) 4 : 5 : 10

**4).**

**Each edge of a cube is decreased by 30%. Find the decrease in its volume.**

a) 62.5

b) 63.5

c) 67.7

d) 62.7

e) 65.7

**5).**

**The circumference of the semicircle is 180 cm. If the side of a square is 60% more than the diameter of the circle, then what is the perimeter of the square?**

a) 368cm

b) 464 cm

c) 486 cm

d) 448 cm

e) 344 cm

**6).**

**The cost price of two Sofas are equal. One Sofa is sold at a profit of 30% and the other one for Rs. 5504 less than the first one. If the overall profit earned after selling both the Sofas is 14%, what is the cost price of each Sofa?**

a) Rs. 17000

b) Rs.16800

c) Rs.17600

d) Rs.17800

e) Rs.17200

**7).**

**In Jar X, 180 litres milk was with 36 litres water. Some of the mixture was taken out from Jar X and put in jar Y. If after adding 6 litres of water in the mixture, the ratio of milk to water in Jar Y was 5 : 2, then what was the amount of mixture that was taken out from Jar X (in litres)?**

a) 24

b) 54

c) 30

d) 36

e) 42

**8).**

**The ratio of the monthly salary of Omana to that of Prakash is 7 : 9. Omana and Prakash both save 20% and 40% of their respective monthly salary respectively. Omana invests ยฝ of his savings in PPF and Prakash invests 7/9 of his savings in PPF. If Omana and Prakash together saved Rs. 17500 in PPF, what is Prakashโs monthly salary?**

a) Rs. 72000

b) Rs. 36000

c) Rs. 45000

d) Rs. 35000

e) Rs. 54000

**9).**

**Raja invested Rs. P in a scheme X offering simple interest at 10% pa for two years. He invested the whole amount he received from scheme X in another scheme Y offering simple interest at 12% pa for five years. If the difference between the interest earned from schemes X and Y was Rs. 1300, what is the value of P?**

a) Rs. 2500

b) Rs. 2000

c) Rs. 3000

d) Rs. 2800

e) Rs. 4500

**10).**

**The distance between two cities (โAโ and โBโ) is 569 km. A train from City โAโ at 8 am travels towards City โBโ at 53 kmph. Another train starts from City โBโ at 9 am and travels towards City โAโ at 76 kmph. At what time will the trains meet?**

a) 12:30 pm

b) 1:00 pm

c) 2 :30 pm

d) 1 30 pm

e) 2:00 pm

__Solutions:__**1).**Five years ago, let Arjun’s age be 3x years. Then, Somu’s age = x

Now, according to the question.

(3x +5 + 6)/( x+5+12) = 7/4

or, (3x+11)/( x+17) =7/4

or, 12x + 44 = 7x + 119

or, 5x = 75

:. x = 15

Somu’s age 3 years ago = 15 + (5 – 3) = 17 years

**Answer is: C)**

**2).**Total number of eggs = 24

:. 8 eggs are rotten

:. Remaining eggs = (24 – 8); 16 is not rotten

Now, 2 eggs are randomly selected.

Then n(S) =

^{24}C_{2}= 23 x 12:. n(E)=

^{16}C_{1}ร^{8}C_{1}= 16 ร 8:. P(E)= (16ร8)/( 23 ร12) = 32/69

**Answer is: D)**

**3).**Ratio of profit

= x ร 4 + 2x ร 8 : 3x ร4 + (3x/2)ร 8 :

5x ร 4 + (5x/2) ร8 = 20x: 24x: 40x = 5 : 6 : 10

**Answer is: D)**

**4).**We know that increase in volume

=3 ร x + (3x

^{2}/100) + (x^{3}/1002)As there is decrease, put the -ve value of x.

:. Percentage decrease in volume

=3 ร (-30) + [3 ร (-30)

^{2}/ 100] + [(-30)^{3}/100^{2}]= – 90 + 27 – 2.7

= -65.7

Note: If you don’t recall the formula, compound it like.

**Step I**. -30 – 30 + [(-30)(-30)/100]= -51

**Step II.**-51 -30+ [(-51)(-30)/100]

= – 81 + 15.3

= -65.7

**Answer is: E**

**5).**Circumference of the semicircle = r (ฯ+2)

:. r[(22/7)+2] =180

or, r(36/7)=180

r = 35cm

Now, side of the square = 2ร35 ร (160/100)

=2 ร 35 ร 1.60 = 70 ร 1.60 = 112 cm

:. Perimeter of the square = 4 ร 112

= 448 cm

**Answer is: D**

**6).**Let the cost of each Sofa be Rs.x,

Now, according to the question,

2xร(114/100)= [(x ร130)/100] + [(x ร130)/100] โ 5504

or, 2.28x = 2.6x – 5504

or, 0.32x = 5504

:. x= [(5504 ร 100)/32] = 172 ร 100= Rs. 17200

**Answer is: E)**

**7).**The ratio of milk to water in Jar X

= 180 : 36 = 5:1

Now, let 6x litres of mixture be taken out from Jar X and put in Jar Y.

Then, milk in Jar Y = 5x

Water in Jar Y= x

So, 5x/(x+6) = 5/2

or, 10x=(5x + 30)

or, 5x=30,

:. x=6

Hence the mixture that was taken out from Jar X = 6x =6 ร 6 = 36 litres

**Answer is: D)**

**8).**Let Prakash’s monthly salary be 9x and Omana’s 7x.

Then, 1/2 of 20% of 7x +(7/9) of 40% of 9x = 17500

or, 10% of 7x + 40% of 7x = 17500

or, 0.7x + 2.8x = 17500

or, 3.5x = 17500

:. x =Rs. 5000

Hence Prakash’s monthly salary = 9 ร 5000

= Rs. 45000

**Shortcut Method:**

According to the question, 7 + 28 = 17500

:. 90 = (17500/35)ร90 =45000

**Answer is: C)**

**9).**Required difference

= [P+(Pร10ร2)/100] ร [(12×5)/100] โ [(Pร10ร2)/100]

or, [(100P+ 20P)/100] ร (60/100) โ (20P/100) = 1300

or, (120P/100) ร (3/5) – (20P/100)=1300

or, 6P/5 ร 3/5 – 20P/100 = 1300

or, (72P-20P)/100 =1300

or, 52P = 1300 ร 100

:. P=(1300 ร 100)/52

= Rs.2500

**Shortcut Method:**

Suppose Raja invested Rs.100 in scheme X.

Then,

According to the question:

52 =Rs.1300

:. P = 100 = (1300/52) x 100 =Rs.2500

**Answer is: A)**

**10).**The distance covered in (9 am – 8 am) is 1 hour by train โXโ=53 ร 1 = 53 km Remaining distance 569 – 53 = 516 km

Relative speed 76 + 53 =129 kmph

:. They meet after (516/129) = 4 hours

Hence they meet at (9 am + 4 hours) = 1 pm

**Answer is: B)**

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