Quant Quiz ” misc.” for SSC CGL 2016


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 








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