Quant Quiz (Arithmetic) for SSC CGL Tier-II 2016

Q1. Four gallons are drawn from a case full of wine. It is then filled with water. Four gallons of mixture are again drawn and the cask is again filled with water. The ratio of quantity of wine now left in the cask to that of mixture in it is 36 : 49. How much does the cask hold?   
(a) 30 gallons
(b) 25 gallons
(c) 35 gallons
(d) 28 gallons

Q2. For a 800 miles trip, a car travelled half the distance at 80 miles per hour and the other half at 100 miles per hour. What was the average speed of the car? (miles/hour)
(a) 18
(b) 180
(c) 90
(d) 88.88

Q3. Three classes x, y and z take an algebra test. 
The average score in class x is 83
The average score in class y is 76
The average score in class z is 85
The average score of all students in classes x and y together is 79
The average score of all students in classes y and z together is 81
What is the average for all the three classes?  
(a) 81
(b) 81.5
(c) 82
(d) 84.5

Q4. Three years ago, the average age of A and B was 18 years. With C joining them, the average age becomes 22 years. How old is C now? 
(a) 24 years 
(b) 27 years  
(c) 28 years 
(d) 30 years 
S4. Ans.(a)
Sol. Present age of A and B = 21 × 2 = 42 
When C join total age of A, B & C = 66 
Age of C = total age of (A + B + C) = total age of (A + B)  
66 – 42 =24 years 
Q5. There are five delegates attending the meeting. The weight of the first delegate is 200 kg and the weight of the 2nd delegate is 20% higher than the weight of the third delegate, whose weight is 25% higher than the 1st delegate’s weight. The fourth delegate at 350 kgs is 30% lighter than the fifth delegate. Find the average weight of all the five delegates. 
(a) 310
(b) 320
(c) 300
(d) 240
S5. Ans.(b)
Sol. Weight of first delegate =200kg
Weight of 3rd delegate =250kg
Weight of 2nd  delegate =300kg
Weight of 4th  delegate =350kg
Weight of 5th  delegate =500kg
Average weight=1600/5=320kg
Q6. The cost price of 20 articles is equal to the mark price of 15 articles. If he allowed a 10% discount on a mark price then what is the profit percentage? 
(a) 20%
(b) 83%
(c) 23.33%
(d) 25%
S6. Ans.(a)
Sol. ( mark price)/(cost price )=20/30=4/3 
Mark price over the cast price is 33.3% 
Profit factor = [(mark price factor) × (Discount factor)] – 1 
=4/3×9/10 
= 1.2 – 1 = .2 
So profit percentage = 20%  
Q7. If the difference between the CI and SI earned at the end of second year on a sum of money at the rate of 10% pa is Rs. 20, what was the sum?  
(a) Rs 3000
(b) Rs. 2000
(c) Rs. 2500
(d) Rs. 3500
S7. Ans.(b) 
Sol. Difference between the C.I & S.I for the two year 
=P×r/100×r/100 
Where r = rate of interest 
P = total sum of money 
20 × 100 × 100 = P × 10 × 10 
P = 2,000
Q8. The rate of simple interest on a sum of money is 6% pa for the first 3 years, 8% pa for the next 5 years and 10% pa for the period beyond 8 years. If the simple interest accrued for a sum for a total period of 10 years is Rs. 1560, what is the sum?   
(a) 2750
(b) 2000
(c) 1800
(d) 2500
S8. Ans.(b)
Sol. Principal =(total interest×100)/(time × interest rate )
=(1560 × 100)/(6×3 + 8×5 +10×2) = Rs. 2000  
Q9. Anish buys a table and a chair for Rs. 2000. He sells table at a profit of 20% and chair at the profit of 30% and thus he gains 23% profit in whole transaction. Find the cost price of table (in Rs)  
(a) 1400
(b) 1200
(c) 1300
(d) 600
Q10. If 1/3 A=1/4 B=1/5 C then what is (A + B)/(A + B + C) = ? 
(a) 3/4
(b) 7/12
(c) 5/7
(d) 5/12 
S10. Ans.(b)
Sol. 1/3 A=1/4 B=1/5 C 
A : B : C = 3 : 4 : 5 
Required answer =(3 + 4)/(3 + 4 + 5)=7/12
Q11. A + B can do a job in 20 days, B + C can do the same job in 30 days and C + A can do the job in 40 days. In how many days A + B + C can do the same job? 
(a) 14 days 
(b) 15 days 
(c) 12.33 days  
(d) None of these 
S11. Ans.(d)
Sol. Assume total work = 120 units (LCM of 20, 30 and 40) 
Work done/day by (A + B) = 6 units per day 
Work done/day by (B + C) = 4 units day
Work done/day by (A + C) = 3 units per day 
Work done/day by 2(A + B + C) = 13 units per day 
Work done/day by (A + B + C) = 6.5 units per day 
Time required by (A + B + C) to finish the work =120/6.5 
Q12. Ram finishes a work in 7 days. Rahim finishes the same job in 8 days and Robert in 6 days. They take turns to finish the work. Ram worked on the first day, Rahim on the second day and Robert on the third and then again Ram and so on. Who was working on the last day when work got finished?  
(a) Ram
(b) Rahim
(c) Robert 
(d) Rahim and Robert 
S12. Ans.(a)
Sol. Three day’s work =1/7+1/8+1/6=73/168 
Six day’s work =73/84 
Seventh day work =1/7, done by Ram 
Since 73/84+1/7=85/84>1, therefore, Ram was working on the last day
S13. Ans.(d)
Sol. Since both Manoj and Ravi are running for the same time, T is constant. Hence, ratio of distance covered by them will be same as ratio of their speed.
So, AX/BX = speed of Manoj/Speed of Ravi =60/40=3∶2   
Q14. After two successive rises, the salary of Eckhart Tolle, working in a BPO company became equal to 15/8 times of his initially salary. By how much percent was the salary raised second time if the first time rise in salary was half of the rise in second time in percent?
(a) 82.5%
(b) 60%
(c) 50%
(d) Can’t be determined
S14. Ans.(c)
Sol. Best way is to go through convenient options.
1+1/4×1=5/4  (∴1/4⟶25%)
5/4+1/2×5/4=15/8  (1/2⟶50%)
Hence option (c) is correct.
Q15. A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5: 3. If he sells the blended variety at Rs 31 per kg, then his gain percent is
(a).65.33%
(b).66.13%
(c).68.14%
(d).70.15%
S15. Ans.(a)
Sol. Suppose he bought 5 kg and 3 kg of tea.
Cost Price = Rs. (5 x 18 + 3 x 20) = Rs. 150.
Selling price = Rs. (8 x 31) = Rs. 248.
Profit = 248 -150 = 98
So, Profit % = (98/150) * 100 = 65.33%

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