Quantitative Aptitude: Inequalities Quiz

Dear Readers,

1. Quantity I: The age of teacher, if the average age of 36 students is 14. When teacher’s age is included the average increases by 1.
   Quantity II: The age of teacher, if the average age of 19 students is 35. When teacher’s age is included the average increases by 0.5.
   A) Quantity I > Quantity II
   B) Quantity I ≥ Quantity II
   C) Quantity II > Quantity I
   D) Quantity II ≥ Quantity I
   E) Quantity I = Quantity II or Relation cannot be established
   
   
2. Quantity I: Profit Percentage , if Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6.
   Quantity II: Profit Percentage, if 100 toys are bought at the rate of Rs. 350 and sold at the rate of Rs. 48 per dozen.
   A) Quantity I > Quantity II
   B) Quantity I ≥ Quantity II
   C) Quantity II > Quantity I
   D) Quantity II ≥ Quantity I
   E) Quantity I = Quantity II or Relation cannot be established
   
   
3. Quantity I: On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:
   Quantity II: A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. The selling price is:
   A) Quantity I > Quantity II
   B) Quantity I ≥ Quantity II
   C) Quantity II > Quantity I
   D) Quantity II ≥ Quantity I
   E) Quantity I = Quantity II or Relation cannot be established
   
   
4. Quantity I: A and B together can do a piece of work in 4 days. If A alone can do the same work in 6 days, then B alone can do the same work in?
   Quantity II: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
   A) Quantity I > Quantity II
   B) Quantity I ≥ Quantity II
   C) Quantity II > Quantity I
   D) Quantity II ≥ Quantity I
   E) Quantity I = Quantity II or Relation cannot be established
   
   
5. Quantity I: A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed of the tour is:
   Quantity II: A went from P to Q with the speed of 60km/hr. and return back with the speed of 90km/hr. Find the average speed.
   A) Quantity I > Quantity II
   B) Quantity I ≥ Quantity II
   C) Quantity II > Quantity I
   D) Quantity II ≥ Quantity I
   E) Quantity I = Quantity II or Relation cannot be established
   
   
6. Quantity I: The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:
   Quantity II: Find the speed of a train which passes a tree in 12 seconds. The length of the train is 264m.
   A) Quantity I > Quantity II
   B) Quantity I ≥ Quantity II
   C) Quantity II > Quantity I
   D) Quantity II ≥ Quantity I
   E) Quantity I = Quantity II or Relation cannot be established
   
   
7. Quantity I: A and B started a business by investing Rs. 20000 and Rs. 35000 respectively. Find the share of B out of an annual profit of Rs. 3520.
   Quantity II: X and Y invested in a business. Their profit ratio is 2:3. If X invested Rs. 4000. Find the amount invested by Y?
   A) Quantity I > Quantity II
   B) Quantity I ≥ Quantity II
   C) Quantity II > Quantity I
   D) Quantity II ≥ Quantity I
   E) Quantity I = Quantity II or Relation cannot be established
   
   
8. Quantity I: The age of P is twelve times that of her daughter Q. If the age of Q is 3 years, what is the age of P?
   Quantity II: The ratio between the present ages of A and B is 2:3. 4 years ago the ratio between their ages was 5:8. What will be A’s age after 7 years?
   A) Quantity I > Quantity II
   B) Quantity I ≥ Quantity II
   C) Quantity II > Quantity I
   D) Quantity II ≥ Quantity I
   E) Quantity I = Quantity II or Relation cannot be established
   
   
9. Quantity I: The difference between SI and CI compounded annually on a certain sum of money for 2 years at 8% per annum is Rs. 12.80. Find the principal.
   Quantity II: A sum fetched a total simple interest of Rs. 800 at the rate of 8 %per annum in 5 years. What is the sum?
   A) Quantity I > Quantity II
   B) Quantity I ≥ Quantity II
   C) Quantity II > Quantity I
   D) Quantity II ≥ Quantity I
   E) Quantity I = Quantity II or Relation cannot be established
   
   
10. There are 5 Brown balls, 4 Blue balls & 3 black balls in a bag .Four balls are chosen at random
    Quantity I: The probability of their being 2 Brown and 2 Blue ball Quantity
    Quantity II: The probability of their being 2 Brown, 1 Blue & 1 blacks
    A) Quantity I > Quantity II
    B) Quantity I ≥ Quantity II
    C) Quantity II > Quantity I
    D) Quantity II ≥ Quantity I
    E) Quantity I = Quantity II or Relation cannot be established

Solution:

1. Option A

Solution: 
I A=a +or – nd
14+ (37*1) =14+37=51yrs.
II 35 + (20*0.5) =35+ 10=45yrs.

2. Option A

Solution: 
I If the no of article bought is LCM of 6 and 5 is 30
CP of 30 articles =5/6*30=Rs25
SP of 30 articles =6/5*30=Rs36
Profit 36-25=11
Profit %ge =11/25 *100=44%
II CP of 1 toy =350/100=3.50
SP of 1toy = 48/12 =4.
Profit=4-3.5=0.5.
Profit %ge (0.5/3.5) *100=14 2/7%

3. Option C

Solution: 
I. C.P. of 12 balls = S.P. of 17 balls = Rs.720.
CP of 1 ball = 720/12=Rs60.
II. SP =85% of 1400
=85/100*1400
=Rs1190.

4. Option A

Solution: 
I. B work= 1/4 – 1/6 = 2/24 ==> 12 days
II.  A’s 1hr work 1/4 .
(B+C’s) 1 hr work 1/3.
(A+C’s) 1hr work 1/2.
A+B+C 1hr work = 1/4+1/3=7/12.
B’s work =7/12 – 1/2=1/12
12hours.

5. Option C

Solution: 
I. Total time taken = (160/64 + 160/80) =9/2hrs
Then avg speed =320/(9/2)
=320*2/9= 71.11km/hr.
II. (2*60*90)/150=72km/hr.

6. Option A

Solution: 
I. Let the speed of two trains be 7x and 8x.
400/4=100
8x=100==>x=12.5.
Then speed of first train =7*12.5 =87.5km/hr.
II. Length of the train = 264m.
Time taken to pass the tree = 12 seconds.
Speed of the train = 264/12 m/sec = 22 m/sec = 22 * 18/5 km/hr = 79.2 km/hr.

7. Option C

Solution: 
I Ratio 20:35=4:7
11 == 3520
7 ?==>Rs2240.
II 4000/y = 2/3
y = 6000.

8. Option A

Solution: 
I 
Ratio P:Q 12:1
1…….== 3
12 ? == 12*3 =36years.
II 
(5x+4)/(8x+4) =2/3
15x+12 = 16x+8
x=4.
A’s age 4 yrs ago 5*4=20
Then A’s age after 7yrs is 20+4+7=31yrs.

9. Option E

Solution: 
I SI-CI=Pr2/100.
P*82/100=12.8
64P/(100*100)=12.8
P=Rs2000.
II SI=Pnr/100
800=P*8*5/100
P=800*100/40
=Rs2000.

10. Option C

Solution: 
I. (5c2 * 4c2)/12c4 = 60/495=4/33
II. (5c2 * 4c1 *3c1)/12c4 =120/95=8/33