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 - Part II

Directions (1- 5): The following pie-chart shows the sources of funds to be collected by the National Highways Authority of India (NHAI) for its Phase II projects. Study the pie-chart and answers the question that follow.

Sources of funds to be arranged by NHAI for Phase II projects (in Rs. crores)

1. Nearly about 20% of the funds are to be arranged through:

A. SPVS 

B. External Assistance

C. Annuity 

D. Market Borrowing

2. If NHAI could receive a total of Rs. 9695 crores as External Assistance, by what percent (approximately) should it increase the Market Borrowing to arrange for the shortage of funds?

A. 4.5 % 

B. 7.5 %

C. 6 % 

D. 8 %

3. If the toll is to be collected through an outsourced agency by allowing a maximum 10% commission, how much amount should be permitted to be collected by the outsourced agency, so that the project is supported with Rs. 4910 crores?

A. Rs. 6213 crores 

B. Rs. 5827 crores

C. Rs. 5401 crores 

D. Rs. 5316 crores

4. The central angle corresponding to Market Borrowing is

A. 52° 

B. 137.8°

C. 187.2° 

D. 192.4°

5. The approximate ratio of the funds to be arranged through Toll and that through Market Borrowing is

A. 2:1 

B. 1:6

C. 3:11 

D. 2:5

Directions (6 – 10): The following line graph gives the ratio of the amounts of imports by a company to the amount of exports from that company over the period from 1995 to 2001.

Ratio of Value of Imports to Exports by a Company over the Years.

6. If the imports in 1998 were Rs. 250 crores and the total exports in the years 1998 and 1999 together was Rs. 500 crores, then the imports in 1999 was?

A. Rs. 250 crores 

B. Rs. 300 crores

C. Rs. 357 crores 

D. Rs. 420 crores

7. The imports were minimum proportionate to the exports of the company in the year ?

A. 1995 

B. 1996

C. 1997 

D. 2000

8. What was the percentage increase in imports from 1997 to 1998?

A. 72 

B. 56

C. 28 

D. Data inadequate

9. If the imports of the company in 1996 was Rs. 272 crores, the exports from the company in 1996 was?

A. Rs. 370 crores 

B. Rs. 320 crores

C. Rs. 280 crores 

D. Rs. 275 crores

10. In how many of the given years were the exports more than the imports?

A. 1 

B. 2

C. 3 

D. 4

Answers:
1. Answer: (B)
20% of the total funds to be arranged = Rs. (20% of 57600) crores
= Rs. 11520 crores = Rs. 11486 crores. (Approx)
Rs. 11486 crores is the amount of funds to be arranged through External Assistance

2. Answer: (C)
Shortage of funds arranged through External Assistance = Rs. (11486 - 9695) crores
= Rs. 1791 crores.
Increase required in Market Borrowing = Rs. 1791 crores.
Percentage increase required = {[(1791 / 29952) ] x 100}% = 5.98%  = 6%. (Approx)

3. Answer: (C)
Amount permitted = (Funds required from Toll for projects of Phase II) + (10% of these funds)
= Rs. 4910 crores + Rs. (10% of 4910) crores
= Rs. (4910 + 491) crores
= Rs. 5401 crores.

4. Answer: (C)
Central angle corresponding to Market Borrowing =[(29952/57600)] x 360º = 187.2º

5. Answer: (B)
Required ratio = 4910/29952= 1/6.1 = 1/6 (Approx)

6. Answer: (D)
The ratio of imports to exports for the years 1998 and 1999 are 1.25 and 1.40 respectively.
Let the exports in the year 1998 = Rs. x crores.
Then, the exports in the year 1999 = Rs. (500 - x) crores.
1.25 = 250/x
x = 250 /1.25 = 200 ( Using ratio for 1998
Thus, the exports in the year 1999 = Rs. (500 - 200) crores = Rs. 300 crores.
Let the imports in the year 1999 = Rs. y crores.
Then, 1.40 = y / 300
y = ( 300 * 1.40 ) = 420
Imports in the year 1999 = Rs. 420 crores.

7. Answer: (C)
The imports are minimum proportionate to the exports implies that the ratio of the value of imports to exports has the minimum value.
Now, this ratio has a minimum value 0.35 in 1997, i.e., the imports are minimum proportionate to the exports in 1997.

8. Answer: (D)
The graph gives only the ratio of imports to exports for different years. To find the percentage increase in imports from 1997 to 1998, we require more details such as the value of imports or exports during these years.
Hence, the data is inadequate to answer this question.

9. Answer: (B)
Ratio of imports to exports in the year 1996 = 0.85.
Let the exports in 1996 = Rs. x crores.
Then, 272/x = 0.85
x = 272 / 0.85= 320
Exports in 1996 = Rs. 320 crores.

10. Answer: (D)
The exports are more than the imports imply that the ratio of value of imports to exports is less than 1.
Now, this ratio is less than 1 in years 1995, 1996, 1997 and 2000.

Thus, there are four such years.

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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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Profit and Loss Quiz on Previous Year's Question

1.   A piece of land came to a person through three middleman each gaining 20%. If the person purchased the land for Rs. 3,45,600 the original cost of the land was
(a) Rs. 1,00,000                           

(b) Rs. 1,50,000
(c) Rs. 1,75,000                           

(d) Rs. 2,00,000

2.  By what per cent must the cost price be raised in fixing the sale price in order that there may be a profit of 20% after allowing a commission of 10%?
(a) 25                                           

(b) 133 1/3
(c) 33 1/3                                    

(d) 30

3.   A cloth merchant sold half of his cloth at 20% profit, half of the remaining cloth at 20% loss and the rest was sold at his cost price. In the total transaction, his gain or loss will be
(a) 5% profit                              

(b) Neither loss nor gain
(c)5% loss                                   

(d) 10% profit 

4.    Ramesh bought 10 cycles for ` 500 each. He spent ` 2000 on the repair of all cycles. He sold five of them for ` 750 each and the remaining for ` 550 each. Then the total gain or loss % is
(a) Gain of 8  1/3 %                  

(b) Loss of 8 1/3 %
(c) Gain of 7  2/3 %                  

(d) Loss of 7 1/7%

5.    If the cost price of 12 oranges is equal to selling price of 10 oranges, then the percentage of profit is
(a) 16  2/3 %                              

(b) 20%
(c) 18%                                        

(d) 25%

6.    The selling price of 10 oranges is the cost price of 13 oranges. Then the profit percentage is
(a) 30%                                         

(b) 10%
(c) 13%                                         

(d) 3%

7.   A man buys 12 articles for Rs. 12/- and sells them at the rate of Rs. 1.25 per article. His gain percentage is:
(a) 20                                           

(b) 25
(c) 15                                            

 (d) 18

8.   A man bought oranges at the rate of 8 for Rs 34 and sold them at the rate of 12 for Rs 57. How many oranges should be sold to earn a net profit of Rs  45? 
(a) 90                                            

(b) 100
(c) 135                                          

(d) 150

9.    A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is
(a) 99 : 125                                 

(b) 25 : 37
(c) 50 : 61                                     

(d) 45 : 56

10.     How much percent above the cost price should a shopkeeper mark his goods so as to earn a profit of 32% after allowing a discount of 12% on the marked price?
(a) 50%                                        

(b) 40%
(c) 60%                                        

(d) 45%

Answer with Explanation:

1.       (d) 

2.       (c) Let the CP = Rs. 100

Then, SP = Rs. 120

Let the marked price = Rs. x

Then, 90% of x = Rs. 120

= x = [(120 x 100)]/90 = 133  1/3

Hence, the marked price is 33  1/3 % above the cost price. 

3.       (a) Total CP = Rs. 100

Total SP =

= Rs. (60 + 20 +25)

= Rs. 105

\ Gain = 5%

4.       (d) Total actual C.P.

= Rs. (500 x 10 + 2000)

= Rs. 7000

Total S.p.

= Rs. (5 x 750 + 5 x 550)

= Rs. 6500

Loss = 7000-6500=  Rs. 500

Loss percent =( 500/700) x 100 = 50/7 = 7 1/7 %

5.        (b) Let C.P of each orange be Re. 1

Then C.P. of 10 oranges = Rs. 10

S.P. of 10 oranges = Rs. 12

Gain % = 20% 

6.       (a) Let the CP of 1 orange = Re. 1

\ CP of 10 oranges = Rs. 13

\ Gain percent = ( 13 – 10)/10  = 100

= 30%

7.       (b) Total Profit = 15 – 12 = Rs. 3

% gain =( 3/12) x 100 = 25% 

8.       (a) Let the man buy 24 (LCM of 8 and 12) oranges.

\ C.P. of 24 oranges =  (34/8) x 24

= Rs. 102

S.P. of 24 oranges

=( 27/12) x 24  = Rs. 114

Gain = 114 – 102 = Rs. 12

 Rs. 12 º 24 oranges

\ Rs. 45 º ( 24/12) x 45

90 oranges 

9.       (d) Let the printed price of the book be Rs. x.

\ Selling price = 90% of x = Rs. 9x/10

If the CP of the book be Rs. y. then,

Y + 112/100 = 9x/10

y/x = 9/10) x 100/112 = 45/56

10.   (a)

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