Dear maths lovers,It is impossible to study maths properly by just reading and listening. For that, we are providing here Quant Quiz of 15 Questions on Algebra in accordance with the syllabus of SSC CGL. So, practise, practise & more practise.We have also provided Study Notes and quizzes on all the topics.

**Q1. LCM of first 100 natural numbers is N. What is the LCM of first 105 natural numbers ?**

(a) 5! × N

(b) 10403 N

(c) 105N/103

(d) 4N

**Q2. Statistics show that 20% of smokers get lung cancer and 80% of lung cancer patients are smokers. If 30% of the population smokes, then the percentage of population having lung cancer is**

(a) 4

(b) 3

(c) 8

(d) 7.5

**Q3. In solution of sugar and water the ratio of sugar and water by weight is 1: 4. This solution is heated and in the process it loses 50% weight. What is the ratio of weight of sugar and water in the final mixture ?**

(a) 4:1

(b) 2:1

(c) 2:3

(d) 3.5:2

**Q4. A cloth store is offering “Buy 3, get 1 free.” What is the net percentage discount being offered by the store ?**

(a) 25%

(b) 20%

(c) 33.33%

(d) 30%

**Q5. A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he had sold. What is the current proportion of water to milk ?**

(a)2:3

(b)3:2

(c)2:1

(d)3:4

**Q6. How many litres of fresh water should be mixed with 30 litres of 50% milk solution so that resultant solution is a 10% milk solution ?**

(a)120

(b)100

(c)50

(d)130

**Q7. Total expenses at a hostel is partly fixed and partly variable. When the number of students is 20, total expense is Rs. 15,000 and when the number of students is 30, total expense is Rs. 20,000. What will be the expense when the number of students is 40 ?**

(a)25,000

(b)40,000

(c)30,000

(d)26,000

**Q8. A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. If all of them work together for 6 hours, how many books will be printed ?**

(a) 60,000

(b) 1,80,000

(c) 1,85,000

(d) 2,85,000

**Q9. How many zeroes will be there at the end of N = 18! + 19! ?**

(a) 3

(b) 4

(c) 5

(d) Cannot be determined

**Q10. Some articles are purchased for Rs. 450. 1/3 rd of the articles are sold at a loss of 10%. At what percentage profit should the remaining articles be sold to obtain a net profit of 20% on the whole transaction?**

(a)35%

(b)20%

(c)10%

(d)40%

**Q11. Saurabh Tripathi travels from Delhi to Lucknow at a speed of 75 km/h and returns to Delhi at a speed of 50 km/hr. He again leaves for Lucknow immediately at a speed of 30 km/hr and returns back to Delhi at a speed of 60 km/hr. What is his average speed for the entire journey ?**

(a) 54 km/hr

(b) 48 km/hr

(c) 56 km/hr

(d) Cannot be determined

**Q12. Vinit has to cover a certain distance of 7 km in 1 h 12 minutes. If he walks some distance at 4 km/h and rides a horse for some distance at 10 km/h, he reaches his destination in time. How far should be walk on foot ?**

(a) 14/3 km

(b) 11/3 km

(c) 13/3 km

(d) 10/3 km

**Q13. Two trains have respective lengths as 230 m and 190 m. They cross each other completely in 21 s, if they are travelling in the opposite direction. And in 42 s, if they are travelling in the same direction. Find the ratio of the speeds of the two trains.**

(a) 3 : 1

(b) 4 : 1

(c) 3 : 1

(d) None of these

**Q14. In the given figure, O is the centre of the circle, ∠AOC = 160°. If AB = AC, then find ∠BAC.**

(a) 45°

(b) 20°

(c) 60°

(d) 75°

**Q15. In the given figure, O is the centre of the circle, OQ = QR and ∠QRO = 15°. Find ∠ QOP.**

(a) 120°

(b) 150°

(c) 135°

(d) 105°

**Solutions**

**S1. Ans.(b)**

**Sol.**

**If we look at the numbers 100 < N ≤ 105, we see only 101 and 103 do not have their factors in N (because these are primes). So, obviously the new LCM will be 101 × 103 × N.**

**S2. Ans.(d)**

**Sol.**

**Assume that the total population is 100.**

**30 people smoke, and out of them 6 people will be having lung cancer.**

**This 6 represents 80% of lung cancer patients (because they smoke).**

**Hence, total percentage of population having lung cancer = 6/80×100=7.5%**

**S3. Ans.(c)**

**Sol.**

**■(Sugar&:&Water@1&:&4)**

**Let the weight of solution be 5 units**

**Weight of Sugar = 1 unit**

**After heating weight of solutions = 2.5 unit**

**So, weight of water remaining = 2.5 – wt. of Sugar**

**= 1.5 unit**

**Ratio = 1 : 1.5**

**= 2 : 3**

**S4. Ans.(a)**

**Sol.**

**Suppose price of one article is Re 1.**

**So, price of 4 articles = Rs. 4.**

**Now the whole scene can be understood as —**

**We are paying only Rs. 3 at the place of Rs. 4.**

**So, discount = Re1.**

**So, discount percentage = ¼ (discount/total price) = 25%**

**Also, you can use trice → (free item)/(Total item)×100**

**=1/4×100=25%**

**S5. Ans.(a)**

**Ratio of Milk and Water**

**M :W**

**80:20**

**1/4 th of the mixture is sold, Milk and Water both will be reduced by 25%**

**To replenish the quantity, we will add 25 litres of water.**

**So, New ratio**

**M :W**

**60:40**

**3:2**

**Water : Milk = 2 : 3**

**S6. Ans.(a)**

**Sol.**

**50% of milk solution will have milk and water in the ratio**

**1 : 1**

**Final ratio → 10:90**

**1 :9**

**Now,**

**2r=30l (Volume of mixture)**

**1r = 15ℓ**

**8r = 120l.**

**S7. Ans.(a)**

**Sol.**

**Expenses = F + K. V; where F is the fixed cost and V is the number of students.**

**Rs. 15,000 = F + K.20 ……………(i)**

**Rs. 20,000 = F + K.30 ……………..(ii)**

**Solving (i) and (ii),**

**Rs. 5,000 = 10. K ⇒ K = Rs. 500**

**So, F = Rs. 5000**

**So, F + 40 K = Rs. 5,000 + 40 × 500 = Rs. 25,000**

**S8. Ans.(c)**

**Sol.**

**Machine P can print 100000/8=12500 copies per hour.**

**Machine Q can print 100000/10=10000 copies per hour.**

**Machine R can print 100000/12=8333 1/3 copies per hour.**

**All of them together can print = 30833 1/3 copies per hour.**

**Therefore, in 6 hours they can print = 30833.33×6=185000 copies.**

**Hence, option (c) is the answer.**

**S9. Ans.(b)**

**Sol.**

**18! +19!= 18!(1+19)= 18! * 20**

**Since number of zeroes in 18! is 3 and clearly 20 has a zero, hence total number of zeroes must be 4.**

**S10. Ans.(a)**

**Sol.**

**Now,**

**(x-20)/30=1/3×3/2**

**(x-20)/30=1/2**

**x=35%**

**S11. Ans.(b)**

**Sol.**

**Average speed of 1st journey = (2×75×50)/125=60 km/hr**

**Average speed for 2nd journey = (2×30×60)/90=40 km/hr**

**Average speed for culture journey = (2×60×40)/100=48 km/hr**

**S12. Ans.(d)**

**Sol.**

**Time taken to cover 7 km = 1 hr 12 min = 6/5 hr**

**So, Speed = 7/((6/5) )=35/6 km/hr**

**Ratio of time → 25: 11**

**Now, 36 r → 6/5**

**1r → 1/30**

**Time taken to walk on foot = 25r**

**=25/30=5/6 hr**

**Distance covered by foot = s × t**

**=4×5/6**

**=10/3 km**

**S13. Ans.(a)**

**Sol.**

**Let the speed of two trains be x m/s and y m/s**

**Case I:**

**In opposite direction**

**Relative speed will be = (x+y) m/s**

**i.e., (230+190)/(x+y)=21s**

**420/(x+y)=21**

**x+y=20 …..(i)**

**Case 2:**

**In same direction**

**Relative speed =(x-y) m/s**

**i.e., 420/42=x-y. Hence x-y=10 ………(ii)**

**On solving (i) and (ii) we get x=15 m/s, y=5 m/s,**

**Therefore the ratio = 3: 1**

**S14. Ans.(b)**

**Sol.**

**∠AOC = 160°**

**So, ∠ABC = 80° [Angle at the circumference]is half of the centre by the same Arc.**

**Also, AB = AC**

**So, ∠ABC = ∠ACB = 80°**

**So, ∠BAC = 20°**

**S15. Ans.(a)**

**Sol.**

**Given, OQ = QR**

**∠QRO = 15°**

**So, ∠QOR = 15°**

**Also,**

**∠OQP = 30° (Ext. angle of a ∆)**

**Now, OP = OQ = r**

**∠OPQ = ∠OQP = 30°**

**So, ∠QOP = 120°.**

*You may also like to read:*