Special Quant Quiz (Arithmatic) SSC CGL Tier-II 2016

Q1. Anu sold 2 books at Rs. 1.40 each. Her profit on one was 20% and her loss on the other was 20%. Then, she: 
(a) made no gain no loss
(b) Gained 20 paise
(c) Lost 20 paise
(d) lost 12 paise
S1. Ans.(d)
Sol. S.P of 2 books = Rs. 2.80
Over all percentage change
= 20 + (-20) + (20 × (-20))/100=-4 = 4% loss
∴ C.P. = (2.80 × 100)/(100 – 4) = 2.92

⇒ Loss = Rs. 0.12


Q2. A house worth Rs. 150000 is sold by X at 5% profit to Y. Y sells the house back to X at a 2% loss. Then, in the entire transaction:
(a) X gains Rs. 4350
(b) X loses Rs. 4350
(c) X gains Rs. 3150
(d) X loses Rs. 3150
S2. Ans.(a)
Sol. X’s gain = (5-2-(5 × 2)/100)% of 1,50,000

= Rs. 4350.


Q3. A businessman marks his goods in such a way that even after allowing 12.5% discount on cash purchase, he gains 20%. If the cost price of the goods is Rs. 140, the marked price is:
(a) Rs. 162
(b) Rs. 172
(c) Rs. 192
(d) Rs. 198
S3. Ans.(c)
Sol. Suppose marked price = Rs. K
∴ K – 12.5% of K = 140 + 20% of 140
⇒ 87.5% of K = 140 + 28 = 168

∴ K = 16800/87.50 = 192.


Q4. 6 men can complete a piece of work in 12 days. 8 women can complete the same price of work in 18 days, whereas 18 children can complete the piece of work in 10 days. 4 men, 12 women and 20 children work together for 2 days. If only men were to complete the remaining work in 1 day how many men would be required?
(a) 36
(b) 24
(c) 18
(d) Cannot be determined
S4. Ans.(a)
Sol. Males : Females : Children
6 × 12 : 8 × 18 : 18 × 10
72 : 144 : 180
2 : 4 : 5
So, 2 Males = 4 Females = 5 Children
4 Males + 12 Females + 20 Children
= 4 + 6 + 8 = 18 Males
∵ 6 males finished a piece of work in 12 days.
∴ 18 males finished the work = (12 × 6)/18 = 4 days
Work in 2 days = 2/4=1/2
Rest of the work will be finished in a day by 

= 18 × 2 = 36 males


Q5. 2 men alone or three women alone can complete a piece of work in 4 days. In how many days can 1 woman and 1 man together complete the same piece of work?
(a) 6 days
(b) 24/5 days
(c) 12/1.75 days
(d) Cannot be determined
S5. Ans.(b)
Sol. 2M = 3W
∴ 1M = 3/2W
∴ 1M + 1W = 3/2W + 1W = 5/2W

Number of days = (3 × 4)/(5/2 )=24/5 days


Q6. Ram sets out to cycle from Delhi to Mathura and at the same time Suresh starts from Mathura to Delhi. After passing each other, they complete their journeys in 9 and 16 hours, respectively. At what speed does Suresh cycle if Ram cycles at 16 km per hour?
(a) 12 km/h
(b) 16 km/h
(c) 14 km/h
(d) None of these
S6. Ans.(a)
Sol. (Ram’ s speed)/(Suresh’ s speed)=√(T2 )/√(T1 )=√16/√9=4/3.
∴ Suresh’s speed = 3/4 Ram’s speed

=3/4×16 = 12 km/h.


Q7. A train 300 metres long is running at a speed of 90 km/h. How many seconds will it take cross a 200 metres long train running in the same  direction at a speed of 60 km/h?
(a) 70 seconds
(b) 60 seconds
(c) 50 seconds
(d) None of these
S7. Ans.(b)
Sol. Here, L1 = 300 m, L2 = 200 m, 
s1 = 90 km/h and s2 = 60 km/h
∴ s1-s2 = 90 – 60 = 30 km/h = 30 × 5/18 m/s
∴ Time taken = (L1+ L2)/(s1- s2 )=(300 + 200)/(30 × 5/18)

= (500 × 18)/(30 × 5) = 60 seconds.


Q8. A person covers half of his journey at 30 km/h and the remaining half at 20 km/h. The average speed for the whole journey is:
(a) 25 km/h
(b) 28 km/h
(c) 32 km/h
(d) None of these 
S8. Ans.(d)
Sol. Here s1 = 30 and s2 = 20.
∴ Average speed = (2s1 s2)/(s1  + s2 )

= (2 × 30 × 20)/(30 + 20) = 24 km/h.

Q9. Two trains, one 160 m and other 140 m long, are running in opposite directions on parallel rails. The first train at 77 km/h and the other train at 67 km/h. How long will they take to cross each other.
(a) 7 seconds
(b) 7.5 seconds
(c) 6 seconds
(d) 10 seconds
S9. Ans.(b)
Sol.
Required time = (160 + 140)/((77 + 67)× 5/18)=(300 × 18)/(144 × 5)
= 7.5 seconds.
 
Q10. A car driver leaves Bangalore at 8:30 am and expects to reach a place 300 km from Bangalore at 12:30 pm. At 10:30 he finds that he has covered only 40% of the distance. By how much % he has to increase the speed of the car in order to keep up his schedule?
(a) 45 
(b) 40 
(c) 35 
(d) 50 
S10. Ans.(d)
Sol. Distance covered by the car in 2 hours
= (300 × 40)/100 = 120 km
Remaining distance = (300 – 120) = 180 km
Remaining time = (4 – 2) = 2 hours
∴ Required speed = (180/2) = 90 km/h

Increase in the  speed of car = ((90-60)/60) = 50%


Q11. A trader has 50 kg of sugar, a part of which he sells at 10% profit and the rest at 5% loss. He gains 7% on the whole. What is the quantity sold at 10% gain and 5% loss?
(a) 40 kg, 10 kg
(b) 10 kg, 35 kg
(c) 25 kg, 15 kg
(d) 30 kg, 20 kg

Q12. Jagtap purchases 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of Rs. 14.25 per kg. He mixed the two and sold the mixture. Approximately at what price per kg should he sell the mixture to make 30 percent profit?
(a) Rs. 16.30
(b) Rs. 18.20
(c) Rs. 15.60
(d) Rs. 14.80
S12. Ans.(a)
Sol. Cost price of mix=30×11.50+20×14.25/20+30
                                         =12.6

      Selling price =12.6×1.3=16.30

Q13. A container contains 10 litres mixture in which there is 10% sulphuric acid. How much sulphuric acid is to be added to make the solution to contain 25% sulphuric acid?
(a) 2 litres
(b) 1 litre
(c) 4 litres
(d) Data inadequate
S13. Ans.(a)
Sol. Initially container contains sulphuric acid=1 litres
And water=9litres
Let the X litres sulphuric acid dded
According to question=1+X=(10+X) ×.25
So, X=2 litres

Q14.Three students A, B and C play cricket. The runs scored by A and B respectively are in the ratio 3 : 2. B’s runs to C’s runs are also in the same ratio. Together they score 342 runs. Then the runs scored by B are
(a) 216  
(b) 108  
(c) 90   
(d) 171
S14.Ans.(b)
Sol. A : B  = 3 : 2 = 9 : 6
B : C = 3 : 2 = 6 : 4
so A : B : C = 9 : 6 : 4
so Runs scored by B = 6/19 * 342

= 108


Q15.A father is 7 years older than the mother and the mother’s age now is 3 times the age of the daughter. The daughter is 10 years old now. What was the father’s age when the daughter was born? 
(a) 27 years  
(b) 37 years  
(c) 15 years  
(d) 40 years 
S15.Ans.(a)
Sol. Mother’s present age
= 30 years
Father’s present age = 37 year
Father’s age 10 years ago

= 37 – 10 = 27 years



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