**Q2. A and B can do a job alone in 24 days and 96 days respectively. B starts the work and worked for 15 days. Then A joins him and both together completed the work. For how many days did A actually work on the job?**

(a) 107/5 days

(b) 81/5 days

(c) 18 days

(d) 24 days

**Ans.(b)**

**Sol.**In 15 days B completes 15×1/96=5/32 work.

A + B in one day can do 1/24+1/96=5/96 work

After 15 days work still left =1-5/32=27/32 work.

Together they can do it in (27/32×96/5)=81/5

**Q3. Two pipes can fill a cistern separately in 32 minutes and 72 minutes respectively. A waste pipe can drain off 3 litres per minute. If all the three pipes are opened, the cistern fills in 28.8 minutes. What is the capacity (in liters) of the cistern? **

(a) 300

(b) 216

(c) 288

(d) 360

**Ans.(c)**

**Sol.**Let x litre be the capacity of the tank.

x/32+x/72-3=x/28.8⇒x= 288 litres.

**Q4. The base of a right pyramid is an equilateral triangle of side 6 cm. The height of the pyramid is one third of its slant height. What is the volume of the pyramid in cube cm?**

(a) 8√2

(b) 6√3

(c) 8/√3

(d) 9/(2√2)

**Q5. A field is in the form of a rectangle of length 25 metres and width 14 metres. A pit, 6m long, 4m broad and 1m deep is dug in a corner of the field and the earth taken out is evenly spread over the remaining area of the field. The raise in the level of the field is**

(a) 10.8 cm

(b) 7.4 cm

(c) 14.2 cm

(d) 5 cm

**Ans.(b)**

**Sol.**Remaining area of the field = (25 × 14) – (6 × 4) = 326 m2

Raise in the level = (6 × 4 × 1) ÷ 326

≈7.4 cm.

**Q6. Six men earn as much as seven women, two women earn as much as three boys, four boys earn as much as five girls. If a girl earns Rs.16 a week, what does a man earn per week?**

(a) Rs.35

(b) Rs.20

(c) Rs.40

(d) Rs.30

**Ans.(a)**

**Sol.**6 men = 7 women;

2 women = 3 boys;

4 boys = 5 girls;

Now earning of a girls per week = Rs. 16

so Earning of 1 boy = 5/4*16 = 20

Earning of 1 women = 3/2*20 = 30

Earning of 1 man = 7/6*30 = 35

**Q7. A solid is in the shape of a cone surmounted on a hemisphere. The diameter of the hemisphere is 42 cm. volume of the entire solid is 28, 182 cubic cm. What is the height of the combined solid in cm?**

(a) 48 cm

(b) 30 cm

(c) 40 cm

(d) 32 cm

**Q8. Arjun’s expenditure and savings are in the ratio of 5 : 1. His income increased by 20% and his expenditure also increases by 8%. What is the percentage increase in his saving?**

(a) 72%

(b) 64%

(c) 80%

(d) 56%

**Ans.(c)**

**Sol.**Arjun’s expenditure = 5x,

His saving = 1x;

His total income = 5x + 1x = 6x

New income =6×((100 + 20)/100)=7.2x

New expenditure =5×((100 + 8)/100)=5.4x

New saving = 7.2x – 5.4x = 1.8x

Required percent = (1.8x – x)÷x×100=80%

**Q9. A fruit seller bought 100 apples at the rate of Rs. 5 each. He sells 1/4 th of them for 80% profit. 1/10 th of the apples are found to be rotten. He wants to get a overall profit of 49%. A what price he has to sell each of the remaining apples?**

(a) Rs. 7

(b) Rs. 5

(c) Rs. 6.50

(d) Rs. 8

**Ans.(d)**

**Sol.**100 apples CP = 100 × 5 = Rs. 500

25 apples SP =1/4×500×((100 + 80)/100)= Rs. 225

Let Rs x be the SP of each of the remaining (100 – 25 – 10) = 65 apples

∴((65x + 225) – 500)/500=49/100⇒x = Rs. 8

**Q10.The ratio of the number of students studying in Schools A, B and C is 4 : 8 : 3 respectively. If the number of students studying in each of the schools is increased by 80%, 20% and 60% respectively, what will be the new ratio of the number of students in Schools A,**

**B and C.**

(a)8 : 3 : 4

(b)4 : 2 : 3

(c)2 : 3 : 4

(d)None of these

**Ans.(d)**

**Sol.**

Required ratio = (4*180) : (8 * 120) : (3 * 160)

= 3 : 4 : 2

**Q11.A person covered some distance in 24 hours. He covered half the distance by rail @ 75 km per hour and the rest by car @ 45 km/hr. The total distance covered by him was**

(a)900 km

(b)1350 km

(c)675 km

(d)2700 km

**Ans.(b)**

**Sol.**

Let the total distance be 2D. Now,

D/75+D/45=24

D = 675

Total distance = 2 * 675 = 1350

**Q12. ABC is a triangle M and N are two points on AC and BC such that ∠ABC=∠CMN. Given CN = 4 cm; AB = 15 cm and AC = 10 cm. What is the length of MN in cm?**

(a) 7.4 cm

(b) 5.6 cm

(c) 8.2 cm

(d) 6 cm

**Q13. I am three times as old as my son. Five years later, I shall be two and a half times as old as my son. Then my age and my son’s age are respectively:-**

(a) 42 yrs, 14 yrs

(b) 45 yrs, 15 yrs

(c)36 yrs, 12 yrs

(d) 48 yrs, 16 yrs

**Ans.(b)**

**Sol.**

Let the present age of my son = x yrs.

Then,the present age of mine = 3x yrs.

(3x+5)=5/2(x+5)

x = 15 yrs.

Father’s age = 45 yrs.

Son’s age = 15 yrs.

**Q14. What is the area of the triangle formed by the straight lines x = 8, y = 4 and 4x – 8y – 32 = 0?**

(a) 28 sq. units

(b) 64 sq. units

(c) 32 sq. units

(d) 16 sq. units

**Q15. If a + b + c = 13, what is the maximum value of (a-3)(b-2)(c+1)?**

(a) 26

(b) 27

(c) 30

(d) 19

**Ans.(b)**

**Sol.**If x + y + z is constant, the product xyz takes maximum value when each x, y, z takes equal value.

∴ a + b + c = 13

∴ (a – 3) + (b – 2) + (c + 1) = 13 – 3 + 2 + 1 = 9

For the maximum value of (a – 3) (b – 2) (c + 1)

= (a – 3) = (b – 2) = (c + 1) =9/3=3

So, (a-3)(b-2)(c+1)=3×3×3=27