Types of Questions Asked in Exams on Percentage

TYPE 1.
If there is increase of X% and subsequently X% decrease then there is always loss / decrease in the condition.
 

Example. If rohan salary is increase by 50% and subsequently decrease by 50%. How much percentage loss?
Ans. By trick ----  50x50/100= 25% decrease/loss 

TYPE 2.
if A is P% more than B. then B is less than by A  with P/(100+P)x100 

Example:  If radha earning is 25% more than sita. Then sita earning is how many percentage less then by radha?

Ans. By trick ---- 25/(100+25)x100=20%   

TYPE 3. 
If A is P% less than B. then B is more than by A with P/(100-P)x100 

Example: If golu age is 20% less than gita than gita age is how many percentage more than golu?
Ans. By trick ---- 20/(100-20)x100=25%

TYPE 4.
If there is p% increase in price . how much % decrease his consumption so that his expenditure on it does not change.
formula P/(100+P)x100

Example. If petrol price increase by 25%. How much percentage a person reduced his consumption so that his expenditure on it does not increase? 
Ans. 25/(100+25)x100=20%

TYPE 5.
if there is p% decrease in price . how much % increase his consumption so that his expenditure on it does not change.
formula P/(100-P)x100

Example. If there is 30% decrease in eggs price. How much a person increased his consumption so that his expenditure on it does not increase?   
Ans. 30/(100-30)x100=42.85

TYPE 6.

Example. If suman need 36% minimum mark to passed a exam but she score 24% mark and fail by 9 marks. What is the total mark? 
Ans. Difference in % = difference in mark

In that 36%-24%=12%
that is 12%=9marks
so, total mark = 9/12x100= 75

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Quant Quiz

1.    A sum of Rs 731 is distributed among A, B and C, such that A receives 25% more than B and B receives 25% less than C. What is C’s share in the amount?
(1) Rs 172                                  (2) Rs 200                  

(3) Rs 262                                  (4) Rs 272

      

2.    Manoj sold an article for Rs 15000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the selling price?
(1) Rs12,500                              (2) Rs13,500              

(3) Rs12,250                              (4) Rs13,250  

3.    What will be the compound interest accrued on an amount of Rs 10,000 @20p.c.p.a. in two years if the interest is compounded half-yearly?
(1) Rs 4,400                               (2) Rs 4,600               

(3) Rs 4,641                               (4) Rs 4,680  

4.    The average weight of 4 men is increased by 3kg when one of them who weighs 120 kg is replaced by another man. What is the weight of the new man?

     (1) 125 kg                                   (2) 150 kg

     (3) 122 kg                                   (4) 132 kg

5.    B and C together can complete a piece of work in 8 days. A and B can complete the same work in 12 days and A and C can complete the same work in 16 days. In how many days can A, B and C together can complete the work?
(1) 3³⁄₉                                        (2) 7⁵⁄₁₃                      

(3) 7⁵⁄₁₂                                      (4) 3⁵⁄₁₂ 

         

6.    The average speed of a car is 1⁴⁄₅ times the average speed of the bus. A tractor covers 575 km in 23 hours. How much distance the car cover in 4 hours of the speed of the bus is twice the speed of the tractor?

     (1) 340 km                                 (2) 480 km     

     (3) 360 km                                 (4) 450 km     

7.    A pump can fill a tank with water in 2 hours. Because of the leak, it took 2¹⁄₃ hours to fill the tank. The leak can drain all the water of the tank in:
(1) 4¹⁄₃ hours                              (2) 7 hours                  

(3) 8 hours                                  (4)14 hours 

    

8.    A shopkeeper mixed two verities of rice at Rs. 20/kg and Rs. 30/kg in the ratio 2 : 3 and sell the mixture at 10% profit. Find the price per kg at which he sold the mixture?
(1) Rs. 26                                   (2) Rs. 28.8                

(3) Rs. 28                                   (4) Rs. 28.6    

9.    The ratio of the present ages of Anju and Sandhya is 13:17 respectively. Four years ago the ratio of their respective ages was 11:15. What will be the respective ratio of their ages six years hence?
(1) 3:4                                         (2) 7:8                         

(3) 5:4                                         (4) 4:5 

10.  A shopkeeper bought 30kg of wheat at the rate of Rs45 per kg. He sold 40% of the total  quantity at the rate of Rs50 per kg. Approximately, at what price per kg should he sell the  remaining quantity to make a profit of 25% overall?
(1) Rs 54                                    (2) Rs 52                    

(3) Rs 50                                    (4) Rs 60   

Answers with Explanation:

            1. (4)
            Let C's share be Rs x.

            Then, B gets =0.75 x.

            A gets = 1.25×0.75x

            x+0.75x+0.9375x=731

            2.6875x=731

            x=⁷³¹⁄_2.6875 =272

            2. (1)
            SP=Rs15000

            SP after 10% discount= 15000-10%of15000

            = 15000-1500=Rs13500

            Profit on SP= 8%

            CP= ¹³⁵⁰⁰⁄₁₀₈ ×100=Rs 12500

            3. (3)
            CI=10000[{(¹¹⁄₁₀ )×(¹¹⁄₁₀ )×(¹¹⁄₁₀ )×(¹¹⁄₁₀ )}-1]

            4.  (4)

            If the average is increased by 3 kg, then sum of weights 

            increases  by 3 x 4 = 12 kg .

            And this increase in weight is due to the extra weight included 

            due to the inclusion of  new person.

            Weight of new man = 120 + 12 = 132 kg.

            5. (2)
            (B+C)'s 1 day work= ¹⁄₈  ...(i)

            (A+B)'s 1 day's work= ¹⁄₁₂  ...(ii)

            (A+C)'s 1 day's work = ¹⁄₁₆  ...(iii)

            On adding all these three equations,

            2(A+B+C)'s one day's work = ¹⁄₈ +¹⁄₁₂ ¹⁄₁₆ = ^(6+4+3)⁄₄₈ =¹³⁄₄₈ 

            (A+B+C)'s one day's work= ¹³⁄₉₆ 

                ∴A, B and C can complete the work in ⁹⁶⁄₁₃ =7 ⁵⁄₁₃ 

            6. (3)

            Speed of the tractor= ^distance/ _time 

            =⁵⁷⁵⁄₂₃ =25kmph

                ∴speed of bus= 50kmph

                ∴speed of car= ⁹⁄₅ ×50=90kmph

                ∴distance covered by the car in 4 hours= 4×90=360km

            7. (4)

            Work done by the leak in 1 hour = (¹⁄₂ -³⁄₇) = ¹⁄₁₄ 

                ∴leak will empty the tank in 14 hours.

            8. (4)

            CP of mixture = ^(20*2+30*3)⁄₂₊₃ =26

            SP of the mixture = 1.1×26=28.6

            9.(4)

            Let the present ages of Anju and Sandhya be 13x and 17x years 

             respectively. 

                ∴^13x-4⁄_17x-4 =¹¹⁄₁₅ 

            =>187x-44=195x-60

            =>195x-187x=60-40

            =>x=2

                ∴Required ratio= (13×2+6):(17×2+6)

            =4:5

            10.       (4)

            CP of wheat= 30×45=Rs1350

            40% of 30kg =12kg

            SP of 12kg = 12×50 = Rs 600

            For 25% profit, total SP of all the wheat is 1350×¹²⁵⁄₁₀₀ 

            =Rs 1687.5

            Remaining wheat (30-12) = 18kg

             Rate of remaining wheat = ^1087.5⁄₁₈ ≈Rs60                  

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Details of Triangle and its Properties - Part - II

As we all know, a triangle is a shape that consists of three sides and three angles. Taking a look at the triangle's angles often helps us find out what kind of triangle we are dealing with.

Here are some facts to remember:

• The three angles in a triangle always add up to 180⁰
• The three angles of an equilateral triangle are all equal to 60⁰
• Two angles of an isosceles triangle are equal.
• One angle of a right-angled triangle is 90⁰
• All angles of an acute-angled triangle are acute angles, thus smaller than 90⁰
• One angle of an obtuse-angled triangle is obtuse, thus larger than 90⁰ and smaller than 180⁰

•  Click here for Basic Triangle Part - I

If two triangles are congruent they have equal sides, equal areas. 

Condition for congruence:

1. SAS condition

If two sides and the included angle of one triangle is equal to the corresponding sides and included angle of the other triangle, then both triangles are congruent.
AB = DE, BC = EF and ∠B = ∠E, then ΔABC≈ΔDEF

2. ASA condition

If two angles and the included side of one triangle is equal to the corresponding two angles and    the included side of the other triangle, then both triangles are congruent.

If ∠A = ∠D, ∠B = ∠E and AB = DE, then ΔABC≈ΔDEF

3. SSS condition

If three sides of one triangle is equal to the corresponding three sides of other triangle then both    triangles are congruent.

  If AB = DE, AC = DF and BC = EF, then ΔABC≈ΔDEF

4. RHS condition

If the two triangles are right-

angled triangle and hypotenuse and one side of one triangle is equal    to the hypotenuse and corresponding side of other triangle, then both triangles are congruent.

if ∠B =∠E = 90°, AC = DF and AB = DE or BC = EF, then ΔABC≈ΔDEF

Note:  

 i.   All the congruent triangles are similar but all similar triangles are not congruent.

 ii.  The ratio of the areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides.

The following four theorems are most important in solving questions on triangles.

Pythagoras’ theorem: In a right angle triangle the square of the hypotenuse is equal to the sum of the squares of other two sides.

Pythagorean triplet: There are certain triplets which satisfy the pythagoras’ theorem and are commonly, called pythagorean triplet.

 For example: 3, 4, 5;    5, 12, 13;    24, 10, 26;    24, 7, 25;    15, 8, 17

Appolonious theorem: 

In triangle ABC, AD is median, which divides BC into two equal parts. Then,

AB²+AC²=2(AD²+BD²)=2(AD²+DC²)

 Stewart theorem:

In Triangle ABC, AD divides side BC in the ratio m and n. (Here AD need not be median) then, 

m.b²+n.c²=a(d²+mn)

Mean proportionality and Mid Point theorem:

In the first triangle, DE // BC so AD/DB=AE/EC

In the second triangle, D and E are mid points of AB and AC respectively. Which implies, AD/DB=AE/EC=1

Also, DE=1/2BC

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Quant Quiz For SSC Exam

Dear reader here we are providing some question on quant aptitude which can be help in your upcoming exams.
1.    The selling price of 10 oranges is the cost price of 13 oranges. then the profit percentage is :
(1) 30%
(2) 10%          
(3) 13%                               
(4) 3%


2.   A shop man bought pens at the rate of 7 for Rs10 and sold them at the profit of 40%.how many pens would a customer get for Rs 10.
(1) 6                                   
(2) 4
(3) 5                                   
(4) 3

3.   A train running at 36 km/hr passes another train completely in 12 s, which is half of its length, running in the opposite direction at 54 km/hr. If it also passes a railway platform in 1.5 min, what is the length of the platform (in meters)?
(1) 700                               
(2) 860                        
(3) 900                               
(4) 1, 000   
       
4.   Two rice varieties costing Rs 20 per kg and Rs 30 per kg were mixed as 2 : 3 and sold so as to gain 10%. What was the SP of the mixture (Rs/kg)?
(1) 31.2                              
(2) 28.6                       
(3) 30                                 
(4) 26      
        
5.   A circle of radius 8 cm has its radius decreased by 2 cm. What is the approximate percentage decrease in area?
(1) 25%                             
(2) 50%                      
(3) 38%                             
(4) 43.75%   
  
6.   In a school, there are 3600 students. The ratio of boys to girls is 4 : 5. If twenty percent of the boys and sixty percent of the girls like to play hockey, then how many students do not like to play hockey?
(1) 1520                             
(2) 1250                      
(3) 2008                             
(4) None of these

7.   The ratio of the present ages of Sonu and Monu is 7: 6 respectively. Eight years ago the respective ratio of their ages was 5 : 4. What will be Monu’s age four years from now?
(1) 28 years                       
(2) 32 years    
(3) 24 years                       
(4) 30 years    

8.  The sum of three consecutive odd numbers is 20 more than the smallest number. What is the middle number?
(1) 7                                   
(2) 9                
(3) 11                                 
(4) 5   
             
9.   A invests Rs. 24000 to start a business. Four months later B joins him by investing Rs. 31000 and after another two months C joins them by investing Rs. 40000. At the end of one year the business earns a profit of Rs. 12028. What is C's share in the profit?
(1) Rs. 4464                      
(2) Rs. 3844   
(3) Rs. 3720                      
(4) Rs. 3270   

10.  2 men can complete a piece of work in 6 days. 2 women can complete the same piece of work in 9 days, whereas 3 children can complete the same piece of work in 8 days. 3 women and 4 children worked together for 1 day. If only men were to finish the remaining work in 1 day, how many total men would be required?
(1) 4                                   
(2) 8                
(3) 6                                   
(4) 2

Answers with solutions:
1.(1) 
Profit percentage = (13-10)*100/10 = 30%

2. (3) 
The S.P. of 7 pens = 10*140/100 = Rs 14
∴The S.P. of I pens = 14/7 = Rs 2
∴The pens for Rs 10 = 10/2 = 5

3. (1)
Crossing time = l1+ l2 / relative speed
l1 = x
l2 = x/2
Relative speed = 36 + 54 = 90 km/hr = 90 x 5/8 = 25 m/s
Time = 12 sec
12 = x + x/2 / 25
x = 200 m
Now train crossing the platform
l1 = 200 m,    l2 = length of platform = y
Time = 1.5 min = 90 sec
Speed = 36 km/hr = 10 m/s
90 = 200 + y / 10
Y = 700 m

4.  (2) 
CP of the mixture = 20 x 2 + 30 x 3  / 5   = 26
SP = 1.1 x 6 = 28.6

5.  (4) 
Original area of the circle = π (8)2 = 64 π
New area of the circle = π (6)2 = 36 π

% decrease in area = 64 π  - 36 π / 64 π x 100 = 43.75%

6.  (4) 
Total Students in school = 3600
Number of boys = 4/9 x 3600 = 1600
Number of boys who like hockey = 20% of 1600 = 320
Number of girls = 2000
Number of girls who like hockey = 60% of 2000 = 1200
Number of students who do not like hockey = (1600 – 320) + (2000 – 1200) = 2080 

7.  (1)
Let the present ages of Sonu and Monu be 7x and 6x. Now
7x – 8 /6x – 8 = 5/4
x = 4
Present age of Monu = 24 years
Monu’s age four years from now = 24 + 4 = 28 years

8.  (2)
 Let the numbers be x, x + 2 and x + 4. Then
x + (x + 2) + (x + 4) = x + 20
x = 7
So the middle number is 9.

9.  (3)
 The ratio of their investments = 24000 x 12: 31000 x 8 : 40000 x 6 = 36 : 31:30
Since the ratio of investment is also the ratio of profit,
C’s share = 30/97 x 12028 = 3720

10. (2) 
2 M x 6 = 2 W x 9 = 3 C x 8
2 M = 3 W = 4 C
The ratio of efficiency of man, woman and children = 1/2: 1/3: 1/4 = 6: 4: 3
Let the work done by a man, a woman and a children in one day be 6 units, 4 units and 3 units respectively.
So the total work to be done = 2x6x6 = 72 units
Work done by 3 women and 4 children in one day = 3 x 4 + 4x 3 = 24 units
Remaining work = 72 – 24 = 48 units
Number of men required to complete the remaining work in one day = 48/6 = 8

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Quant Quiz For SSC Exam

1.    A man rows 20 km downstream and 16 km upstream taking 4 hours each time. What is the speed of current?
(a) 0.4 kmph
(b) 0.5 kmph
(c) 0.6 kmph
(d) 0.1 kmph

2.    On selling an item for Rs 20 a man gains 25%. In order to gain 40% what will be the increase in it’s selling price.
(a) Rs 3.40
(b) Rs 3 
(c) Rs 2.62
(d) Rs 2.40

3.    The sum of money that will give Rs 2 as simple interest per day at the rate of 8% per annum is
(a) Rs 9125
(b) Rs 7236
(c) Rs 6382
(d) Rs 9262

4.    X can do a piece of work in 20 days and Y can do it in 10 days. They started together, but after 6 days X leaves off. Y will do the rest work in
(a) 1 day 
(b) 2 days
(c) 7/3 days
(d) 3 days

5.    A radio is sold for Rs 990 at a profit of 10%. What would have been the gain or loss in percentage had it been sold for Rs 880?
(a) 19/3%  gain
(b) 17/3% loss
(c) 17% gain
(d) 20/9% loss

6.    In an exam, 60% of the total student passed. If the number of failed students is 320 then the total number of students is
(a) 600 
(b) 700 
(c) 800 
(d) 900 

7.    A cycle is bought for Rs 840 and sold at Rs 920. What is the percentage gain
(a) 10.50%
(b) 8.52%
(c) 7.35%
(d) 9.52%

8.    If Raj’s salary is 30% more than Amar’s salary, the how many percent is Amar’s salary less than that of Raj’s?
(a) 56% 
(b) 23.07%
(c) 50/3%
(d) 50.6%

9.     Find the number of ways in which 5 different beads can be arranged to form a necklace.
(a) 120 
(b) 60 
(c) 30 
(d) 12 

10.  A card is drawn from a pack of playing cards, what is the probability of getting either a red or a red queen?
(a) 4/13  
(b) 7/13 
(c) 1/13 
(d) 1/26 

ANSWERS WITH EXPLNATION :
1. (b)
Speed downstream = 20/4 = 5 kmph
Speed upstream = 16/4 = 4 kmph
Speed of current = 1/2 * (5-4)= 0.5 kmph

2. (d)
SP = 20, gain = 25%
CP = 100/125 * 20 = Rs 16
Now, CP = 16, gain = 40%
SP =  140/100 * 16 = 22.40
Increase = 22.4 – 20 = 2.4

3. (a)
Annual intetest = Rs 365 × 2 = Rs 730
Rate = 8%
Sum = (100 * 730)/8 = Rs 9125

4. (a)
(X + Y)’s 6 days’ work = 6 * (1/20 + 1/10) = 9/10
Remaining work = 1 - 9/10 = 1/10
1/10 work is done 2y Y in 10 * 1/10 = 1 day

5. (d)
Let the CP is Rs x.
Then, x * 110/100  = 990
x = 900
Now CP is Rs 900 and SP is 880.
% loss =  20/900 * 100 = 20/9%

6. (c)
Let the number of student is x out of that 40% have failed.
40/100 * x = 320
x = 320 * 100/40 = 800

7. (d)
CP = Rs 840 and SP = Rs 920
Gain = 920 – 840 = Rs 80
gain percentage = 80/840 * 100 = 9.52%

8. (b);
Amar’s salary is less than of Raj 2y
(R/100 + R * 100)% = (30/(100 + 30) * 100)%
(30/130 *100 )% = 300/13% = 23% APPROX

9. (d)
According to formula:  
Number of arrangements = (5-1)!/2 = 12

10. (b)
26/52 + 2/52 = 28/52 = 7/13

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