## Percentage Math problems with solutions for competitive Exams

Percentage Math problems are always asks in competitive examination. So taking attention we explain some easy and shortcut method solved question.

A percentage is a fraction it means that 1/100, If we find out any percentage of any numbers means that numbers divided by 100 means denominator is 100.

Some important formulae

The meaning of x percentage is any object divide to equal in 100 parts. Now we denoted as below:-

x% = x/100

For Example:- (i) 36% = 36/100 = 9/25

(ii) 0.6% = 6/1000 = 3/500

Transform the fraction a/b as percentage: a/b = (a/b x 100)%

For Example :-(i) 3/4 = 3/4 x 100 = 75%

(ii) 0.8 = 8/10 x 100 = 80%

1. If the value of A is R% more from B then
Hence, Value of B is low from A = {R/(100+R)X100}%

2. If the value of A is is R% low from B, then
Hence, the value of B is more from A = (R/(100-R)x100}%

(i) If any objects rate is increased R%, but expense no increase then,

Consumption reduction in object

Consumption reduction = {R/(100+R X100}%

(ii)If any objects rate is decreased R%, but expense no decrease then,

Consumption increase in object

Consumption reduction = {R/(100-R X100}%

Based on population percentage

Let be population of any city is P and increase yearly on the rate of R%, then

(i) Population after n year = P (1+R/100) n

(ii)Before population n year = P/ (1+R/100) n.

Convert the following below question decimal fractions:

(i) 20%

Solve:- 20/100 = 1/5 = 0.2

(ii)8%

Solve: – 8/100 = 0.08

(iii) 0.25%

Solve: – 25/10000 = 0.0025

1. Convert 9/16 to percentage rate?

Solve:- 9/16 x 100 = 900/16 =56.25%

## Percentage Math Problems with solutions

Question: 1, what percent of 48 are 6?

Solve:- Let x% of 48 = 6

Then, 48 x x/100 = 6

==> 48x/100 =6

==> x = 100 x 6/48 = 12.5%

Question: 2, what percent of 18 are 36?

Solve:- Let x% of 18 = 36

Then, 18 X x/100 = 36

18 x = 100 X 36

x = 3600 /18 = 200

Question: 3, 4:5 =? % .

Solve:- 4:5 = (4/5 X 100)% = 80%

Question: 4, ? of 52% =182.

Solve:- Let the unknown number is x

x X 52/100 =182

==> 52x = 182 X 100

==> x = 350

## Profit and Loss formula and tricks Questions for Students

Profit and Loss formula and tricks:- Selling and buying something like any object it is nature of men’s. But taking profit it get something loss. But how we find out profit and loss. We will cover with some solved questions for students.

Cost price or Purchase Price

When we buy any product then it is called Cost price or purchase price of this product. For Example: – Mohan bought a pen worth Rs.20, and then the cost price of this pen is Rs.20.

Sales price or Selling Price

When we sale or sales by anyone it is called sales price of that product. For Example- Mohan sold his pen Rs.25 rupees, therefore the selling price of this pen will be Rs.25.

Profit or Gain

If the selling price of any product is more than the purchase price then there is profit. For Example:- Mohan bought a pen worth Rs.20 rupees and sold this pen is Rs.25, here he get profit .

Loss

If selling any product get loss or if the selling price is less than the purchase price then this position is get loss. For Example:- If Rajesh bought a pen worth Rs.20 and sales to anyone Rs.15 then he get loss.
Loss = Cost Price – Sales Price

Percentage: Profit and Loss

The meaning of percentage is 100. The meaning of percentage profit and loss is how much profit or loss i made in 100 rupees.

Profit% = profit x 100/CP (Here CP is Cost Price)

Loss% = Loss X 100/CP

It is expense, when we buy any product then we pay tax or commission and transportation it is overhead expense. These expenses added in Cost price.

Discount or Rebate

Discount is remains written with products-price, and given to customers,

Cash Discount:- is given on Cash purchase. Trade Discount: is offered to increase the sales.

## Profit and Loss formula and tricks

Profit & Loss Solved Exaples

Question 1: Cost price of a book is Rs.110 and sold it Rs.123.20 then finds the gain or loss?

Solve:-

Gain = SP – CP = 123.20 – 110 = 13.20

Gain% = Profit x 100/CP = 13.20 x 100/110 = 12%

Question 2: A pen is bought Rs.1960 and sold it Rs.1862. Find out the loss percentage?

Solve:-

Loss = CP – SP = 1960 – 1862 = 98

==>% Loss = 98 x 100/1960 = 5%

Question 3: The purchase price of 15 articles is equal to the selling price of 12 articles, then find out the profit percentage?

Solution:

We have,

SP = 15, CP = 12

Gain = SP- CP = 15 – 12 = 3

Gain% = 3 x 100/12 = 25%

Question 4: A fruit-seller bought 6 bananas in Rs.15 and sold it 4 bananas in Rs.12. Find the profit and loss percentage?

Solution:

Cp of 6 bananas = 15 ==> 1 banana CP = 15/6 = 2.50

Sp of 4 bananas = 12 ==> 1 banana SP= 12/4 = 3

Gain = 3.00 – 2.50 = 0.50

% Gain = 0.50 x 100/2.50 = 20%

Question 5: Aditya sold a cow Rs.525 and get profit 5% then find the cost price of that cow?

Solution:-

CP = 100×525/105 =500

Question 6: After selling a chair Rs.873 get loss 10%, then find the cost price of the dealer?

Solution:-

CP = 100 x 873/90 = 970

Question 7: After selling a watch Rs.2880 a man get 10% loss. If he wants to get 5% profit then find the selling price of this watch?

Solution:-

CP = 100 x 2880/90 = 3200 if 5% profit then

SP = 105 x 3200/100 = 3360

Question 8: If an item is sold 10% profit instead of 5% loss , then dealer get Rs.75 more. Find the cost price of this item?

Solution:-

==>110x/100 – 95x/100 = 75

==> 110x – 95x /100 = 75

==> 15x = 7500

==> x = 7500/15 = 500

Question 9: One man sold two horses on Rs.32500 on each. If he get 15% profit of one horse and other 15% loss then find out the total profit and loss?

Solution:-

Loss% = (15/10)2% = 2.25%

### Profit & Loss Selected Objective Questions

Question 10: A dishonest shopkeeper declare sells any items in cost prise, but he use 900 gram weight instead of 1 kilogram. Find out his profit %.

Solution:

Profit% = {Error X 100/accurate Wt-Error}% = { 100 x 100/(1000-100)}%

==> [100 x 100/900} = 100/9

Question 11: A shopkeeper give discount 10% on printed value on an item, but getting 8% profit what is cost price of that item?

Solution:-

Let the cost price is = 100, SP = 108 and let the printed value is x

==> x x 90% = 108

==> 90x = 108 x 100 = 10800

==> x = 10800/90 = 120 , means 20% more

Question 12: Three respective equivalent discounts are 20%, 10% and 5% and find the discount?

Solution:-

Le to be the print value of product is Rs.100

==> SP= 100 x 80% x 90% x95%= {100 x 80/100 x 90/100 x 95/100}

==> 68.40

==> Equivalent discount = 100 – 68.40 = 31.6%

Question 13: Minal bought a car Rs.250000 and sold it Rs.348000, then find the Percentage gain of this Car?

(a) 40%     (b) 39.2%     (c) 38.4%      (d) 38%     (e) None of these.

Question 14: one trader buys some eggs from Rs.P every dozen and sold it Rs.P/8 each egg. Then find out his profit percentage?

(a) 30%     (b) 40%     (c) 50%      (d) 60%

Question 15: One man sold a book worth Rs.891 and get profit 1/10, then what is cost price of this book?

(a) 850     (b) 800     (c) 810      (d) None of these

Question 16: One trader bought a rice of 26 kilograms in Rs.2470, and he sold 10 kilogram rice Rs.110 per kilograms. At what rate will he sell the remaining rice to earn a profit of Rs.70?

(a) 90     (b) 95    (c) 85      (d) 75     (e) None of these.

#### Profit and Loss basic questions

Question 17: Rajesh buy a cooler for Rs.4700 and spends Rs.800 for repairs on it and sell it or Rs.5800. Then find the gain in percentage?

(a) 20%      (b) 60/11%     (c) 15%        (d) 20%

Question 18: A Man sold an item in Rs. 6759 and loss 25%. If he sold at 15% profit then find out the selling price of that item?

(a) 10530      (b) 9950     (c) 10350        (d) 11340     (e) None of these

Question 19: Sohan bought a pen worth Rs.75 and sold after time it Rs.90. Then find out his profit?

Solution:

==>CP = 75, SP = 90, Gain = SP – CP = 90 – 75 = 15

Question 20: In summer season archana buy a refrigerator in Rs.4000 and it sold it after end of season Rs.3500. Then find the loss?

Solution:-

==> CP= 4000, SP=3500,

Loss= CP-SP = 4000-3500 = 500

Question 21: Mohini bought an air cooler in Rs.5000 and sold it after 6 months in RS.4000, then find his profit and loss percentage?

Solution:-

Loss = 5000 – 4000 = 1000

==>% Loss = 1000 x 100/5000 = 20%

Question 22: Hari buy a cycle for Rs.1400 and sells it at a loss of 15%. Find the selling price of this cycle?
Solution:-

 S.P. = 85% of Rs. 1400 = Rs. 85 x 1400 = Rs. 1190 100

## How to Solve LCM Questions in Hindi

How to solve LCM Questions:- LCM एंड HCF के बारे में जानेगे सभी प्रतियोगी परीक्षाओं में अक्सर सवाल पूछे जाते है ये बहुत ही आसान होते है अगर थोड़ी सी ध्यान दिया जाए तो आप आसानी से हल कर सकते है।

लघुतम समापवर्त्य (LCM ):- वह  छोटी से छोटी संख्या जो दी गई संख्या से आसानी से पूर्णतः विभक्त हो जाए वह दी गई संख्या का LCM कहते है।

जैसे :- 12, 15, 18, 27 का LCM = 3x2x3x2x5x3=540

महत्तम समापवर्त्य (HCF):- दो या दो से अधिक संख्याओं  का महत्तम समापवर्त्य   बड़ी से बड़ी संख्या है जो पूर्णतया विभक्त करती है. जैसे:- 35  तथा 42  का HCF = 7 है|

महतम समापवर्त्य के प्रयोग से लघुतम समापवर्त्य निकालने का तरीका:-

म.स * ल.स. = संख्याओ का गुणनखंड

दो पदों का ल.स.  =  बहुपदों का गुणनफ़ल / बहुपदों का म.स.

अज्ञात बहुपद = म.स X ल.स। / दिया गया बहुपद

LCM एंड HCF पर आधारित कुछ प्रश्न

• 4, 8, 12, 16, 24, 32, 48, 128 का LCM ज्ञात करे.

हल:

प्रथम विधि :- इस विधि को Factor जिसे गुणनखंड विधि

दूसरी विधि : ये भाग की विधि है.

 4,8,12,16,24,32,48,128 2 2, 4,  6,  8,  12,  16, 24, 64 2 1, 2,  3,  4,   6,    8,   12, 32 2 1, 1,  3,  2,  3,   4,   6,  16 2 1, 1,  3,  1,  3,  2,  3,  8 3 1,   1,   1,  1,  1, 2, 1,8 2 1, 1, 1, 1, 1, 1, 1, 4

• 2x2x2x2x3x2x4=384 Ans
• दो संख्याओं का लघुतम समापवर्त्य 1920 तथा महत्तम समापवर्त्य 16  है. यदि इनमे से एक संख्या 128  हो तो दूसरी संख्या ज्ञात करे?

हल:  माना की दूसरी संख्या = x  है.

Then by formulae,

दो संख्याओं का गुणनफल = LCM x HCF

=>x X 128  = 1920 x 16

=>  दूसरी संख्या = 240

• वह छोटी से छोटी संख्या कोण सी है जो 8 , 12 ,18 , 24 में से प्र्तेक से पूर्णतया विभक्त हो जाए .

हल :  पहले हम 8,12, 18, 24 का LCM निकलते है

 8, 12, 18 ,24 2 4, 6, 9, 12 2 2, 3, 9, 6 2 1, 3, 9, 3 3 1, 1, 3, 1

= (2x2x2x2x2x3x3x3x2x3x2x2x2)

= 72 Ans. . .

## Solving linear equations with fractions and variables

Solving Linear Equations with fractions:- It is the part of algebra mathematics.  Linear Equations is the format ax+b =O . This is the very easy chapter. This types of equation is solved by transfer their position left or right , in this case their sign will be changed according to albegra rules.

In this post we are explaining some questions with answers, this is very very important for students. We are explaining easy trick for Solve Linear equations with fractions.

Q1. If 5x = 3x – 10, then find the value of x?
Solve:- We have, 5x = 3x – 10
 5x -3x = 10
 2x = 10
x = (10/2)
x = 5 Ans.

Q2. If 7n-3 = 4, then find the value of n?
Solve:- 7n = 4 + 3
7n = 7
n = 1 Ans

Q3.if 5x = 65-50, find the value of x?
Solve: – 5x = 15
X = 15/5
X = 3 Ans.

Q4. If 4h+34 = 30 then find the value of 2h ?
Solve: we have, 4h + 34 =30
=> 4h = 30-34
=> 4h = -4
=> h = -4/4 = 1-
hence, 2h = 2* -1 = -2 Ans.

Q5, If 6n -63 = 9 then find the value of x ?
Solve:- We have, 6n – 63 =9
=> 6n = 9+63
=> 6n = 72
=> n = 72/6
n = 12 Ans.

Q6, Evaluate the value of x if x +10 = 22
Solve: x + 10 =22
=> x =22-10
=> x = 12 Ans.

Q7, If 2x +3 = 1 then what is the value of x ?
Solve: 2x + 3 =1
=> 2x = 1-3
=> 2x = -2
x = -2/2
x = -1 Ans

Q8, If 6d = 42, then find the value of 11d ?
Solve: we have, 6d =42
=> d =42/6
d =7
hence, 11d = 11 x 7 = 77 Ans.

Q9. If 5a = 15 then find the value of 6a ?
Solve:- we have, 5a = 15
=> a =15/5
a = 3
now find out, 6a (here put the value of a =3, we get
=> 6 x 3 = 18 Ans.

Q10, if 5x = 80, then the value of 17x ?
Solve: we have 5x =80
=> x = 80/5
x =16
now find out 17 x = ?
we put the value of x = 16, we get
=> 17 x 16 = 272 ans

### Linear Equation questions with Solutions

Q11, if 20x -400 = 2400, then what is the value of 5x ?
Solve:- we have
20x – 400 =2400
=> 20x = 2400+400
=> 20x =2800
=> x =2800/20
x = 140

hence, 5x =? ( put the value of x =140 we get
= 5 x 140 =700 Ans

Question 12: If 7n-3 =74, then find the value of n ?

Solution:   ==> 7n = 74+3

==> 7n = 77

==> n = 77/7

==> n = 77

## Age Related Questions in Hindi with answer

Age Related Question in Hindi :- Age Related question in hindi always ask in examination one or more.  We here explaining short and easy tricks for solve age related question in this articles. We will be writing age related questions are many parts. You must read.

Q1.काजल तथा बबीता की आयु का अनुपात 7:3 है, 6 बर्ष के बाद इनकी आयु का अनुपात 5:3 होगा, तो इनकी आयु का अन्तर ज्ञात करे |( The age ratio of Kajal and Babita is 7: 3, after 6 years their age ratio will be 5: 3, then find the difference of their age.)

Solve:- अनुपातिक राशि = x
काजल की आयु = 7x , तथा बबीता की आयु= 3x है,
6 बर्ष के बाद काजल की आयु = 7x +6
6 बर्ष के बाद बबीता की आयु= 3x + 6
by questions,

=> 7x +6/3x+6 =5/3
=> 3 ( 7x + 6 ) = 5 ( 3x + 6)
=> 21x + 18 = 15x + 30
=> 21x-15x =30-18
=> 6x =12
=> x = 12/6
=> x = 2
=> आयु का अन्तर = 7x – 3x = 4x = 4 x 2 = 8 ans .

Q2 रमेश की आयु अपने पुत्र राहुल की आयु से 4 गुना है, 5 बर्ष पहले रमेश की आयु राहुल की आयु से 9 गुनी थी तो रमेश की वर्तमान आयू ज्ञात करें ? (The age of Ramesh is 4 times the age of his son Rahul, 5 years ago Ramesh’s age was 9 times the age of Rahul, then find the current age of Ramesh?
Solve: — माना कि राहुल की वर्तमान आयु = x
तब रमेश की आयु = 4x
5 बर्ष पहले राहुल की आयु = x-5
5 बर्ष पहले रमेश की आयु = 4x-5

by question,
=> (4x-5) = 9 (x-5)
=> 4x- 5 = 9x- 45
=> 4x – 9x = -45 +5
=> -5x = -40
=> 5x = 40
=> x = 40/5
=> x = 8
=> रमेश की वर्तमान आयू = 4x = 4 x 8 = 32 Ans.

Q3. 8 बर्ष पुर्व विशाल की आयु अपने पुत्र रवि की आयु से 4 गुनी थी । 8 बर्ष बाद विशाल की आयु रवि के आयु से दुगुनी हो जाएगी । तो उनके वर्तमान आयु ज्ञात करें ?

(8 Years ago the age of Vishal is 4 times the age of his son Ravi. After 8 years, Vishal’s age will be twice the age of Ravi. So what are their present ages?)

### Age Related Questions in Hindi with solved

Solve: माना कि 8 बर्ष पुर्व रवि की आयु = x
तथा विशाल की आयु = 4x
8 बर्ष बाद रवि की आयु = x + 8
8 बर्ष बाद विशाल की आयु = 4x + 8

by question,
=> ( 4x + 8 ) + 8 = 2 [ (x +8 ) +8 ]
=> 4x + 16 = 2x + 32
=> 4x- 2x = 32- 16
=> 2x = 16
=> x = 16/2
=> x = 8
=> रवि की वर्तमान आयु = x + 8 = 8 + 8 = 16
=> विशाल की वर्तमान आयु = 4x + 8 = 4 x 8 + 8 = 40 Ans.

Q4. A तथा B की आयु का अन्तर 16 बर्ष है, 6 बर्ष पहले B की आयु से तिगुनी थी, दोनो की वर्तमान आयु ज्ञात करें ?

(The difference between the ages of A and B is 16 years, 6 years was three times the age of B, find the present age of both?)
Solve:- माना कि 6 बर्ष पहले B की आयु = x , त्तथा A B की आयु = 3x

6 बर्ष बाद B की वर्तमान आयु = (x + 6)
6 बर्ष बाद A की वर्तमान आयु = (3x + 6)

by question,

=> (3x + 6 ) – (x +6 ) = 16
=> 3x + 6 – x – 6 = 16
=> 2x = 16
=> x = 16/2
=> x = 8
B की वर्तमान आयु = (x + 6) = 8 + 6 = 14 बर्ष
A की वर्तमान आयु = (3x + 6) = 3 x 8 + 6 = 30 बर्ष Ans.

Q5. एक व्यक्ति की आयु अपने पुत्र की आयु के तिगुने से 3 बर्ष अधिक है , यदि 3 बर्ष बाद उस व्यक्ति की आयु अपने पुत्र के आयु के दुगुने से 10 बर्ष अधिक है तो पुत्र की वर्तमान आयु ज्ञात करें ? (A person’s age is 3 years more than his son’s age, if after 3 years that person’s age is 10 years more than his son’s age, then what is the present age of the son?)
Solve:- माना कि पुत्र की आयु = x तथा उस व्यक्ति की आयु = ( 3x + 3)
3 बर्ष पुत्र की आयु= ( x +3)
3 बर्ष स व्यक्ति की आयु = ( 3x + 3)+ 3
by questions,
=> ( 3x + 3)+ 3 = 2 ( x + 3 ) + 10
=> 3x + 6 = 2x + 16
=> 3x – 2x = 16 – 6
=> x = 10
पुत्र की वर्तमान आयु = 10 बर्ष

#### How to solve problems on Ages Easily

Q6. रीना तथा उसकी मां की आयु का योग 49 बर्ष है। 7 बर्ष पुर्व उसकी मां की आयु रीना की आयु से 4 गुनी थी । तो रीना की वर्तमान आयु ज्ञात करे ? (The sum of the ages of Reena and her mother is 49 years. 7 years old his mother’s age was 4 times the age of Reena. Then find the present age of Reena?)
Solve:- माना कि रीना की आयु = x
तथा उसकी मां की आयु= (49 – x )
7 बर्ष पुर्व रीना की आयु = (x – 7)
7 बर्ष पुर्व उसकी मां की आयु = (49 – x – 7 ) = (42 – x )
by questions,
=> 42 – x = 4 ( x – 7 )
=> 42 – x = 4x – 28
=> 5x = 70
=> x = 70/5
=> x = 14
उसकी मां की आयु= (49 – x ) = 49 – 14 = 35 Ans.

Q7. A, B, C की वर्तमान आयु का योग 90 बर्ष है । 6 बर्ष पुर्व उनकी आयु का अनुपात 1:2:3 था । C की वर्तमान आयु ज्ञात करें ? (The sum of the present ages of A, B, C is 90 years. 6 years ago their age ratio was 1: 2: 3. Find the present age of C?)
Solve:- अनुपातिक राशि = x
माना 6 बर्ष पुर्व A की आयु = x , B की आयु = 2x तथा C की आयु = 3x

6 बर्ष बाद A की वर्तमान आयु =( x + 6 )
6 बर्ष बाद B की वर्तमान आयु =( 2x + 6 )
6 बर्ष बाद C की वर्तमान आयु =( 3x + 6 )

by questions,

=> ( x + 6 ) + ( 2x + 6 ) + ( 3x + 6 ) = 90
=> 6x + 18 = 90
=> 6x = 90-18
=> 6x = 72
=> x = 72/6
=> x = 12
C की वर्तमान आयु =( 3x + 6 ) =3 x 12 + 6 = 42 Ans.

Q8. कृष की 5 बर्ष पहले आयु तथा 9 बर्ष बाद आयु का गुणनफ़ल 15 है। कृष की वर्तमान आयु कितनी होगी ? (The age of Krishna 5 years ago and the age of 9 years later is 15. What will be the present age of Krish?
Solve:- माना कि कृष की वर्तमान आयु = x
5 बर्ष पुर्व कृष की आयु = ( x – 5 )
9 बर्ष बाद कृष की आयु = ( x + 9 )

by questions,

=> (x -5 ) ( x + 9 ) = 15
=> X2 +4x – 45 = 15
=> X2 + 4x – 60 = 0
=> X2+ 10 x – 6x – 60 = 0
=> x ( x+ 10 ) – 6 (x + 10)
=> ( x+ 10 ) ( x – 6 )
=> x = 6
Ans

Q9. The current age of A and B is 4: 5, after 5 years, the ratio will be 5: 6, then determine the current age of A?
Solve:- Suppose proportional value is = x
Current age of A = 4x and
Current age of B = 5x

A after 5 years of age = (4x + 5)
Age of B after 5 years = (5x + 5)

by questions,

=> (4x + 5) / (5x + 5) = 5/6
=> 24x + 30 = 25x + 25
=> x = 5
=> A’s current age = 4x = 4×5 = 20 years