September 10, 2024

Preparing for the Navodaya Exam requires a solid understanding of various mathematical concepts, and one such important topic is percentages. In this article  “Percentage questions for Navodaya exam” different types of percentage questions that often appear in the Navodaya Exam are given. By familiarizing yourself with these question patterns and practicing our sample problems, you can gain the necessary skills and boost your overall performance in the exam.

we begins by  the fundamentals of percentages, explaining how to calculate them, convert them into fractions and decimals, and apply them in various real-life scenarios. We’ll provide step-by-step explanations and examples with clarity. Furthermore, we explore the different types of percentage questions commonly encountered in the Navodaya exam, including percentage increase or decrease, profit and loss, discounts, and more.

# Percentage questions for Navodaya exam (Solved Examples)

(i) 120% is equal to   …………………
Sol.  120 % = $\frac{120}{100}$ = 1.2

(ii) Express each of the following statements in the percentage form :
(a) 13 out of 20
(b) 21  out of 30
Solution: (a) $\frac{13}{20}\times&space;100=&space;13&space;\times&space;5=&space;65$

%
(b) $\frac{21}{30}\times&space;100=\frac{21}{3}\times&space;10=7\times&space;10=70$%

(iii) Express the following  fractions as percent :
(a) $\frac{2}{300}$

(b) $\frac{65}{80}$

Sol.  (a) $\frac{2}{300}\times&space;100=&space;\frac{2}{3}=0.67%$

(b) $\frac{65}{80}\times&space;100=&space;\frac{650}{8}=81.25$ %

(iv)  Convert each of the following decimals into a percentage.
(a) 0.08
(b) 0.75
Solution:
(a) 0.08 = (0.08 x 100)% = 8%
(b) 0.75= 0.75 x100 % = 75%

(v) Find :
(a) 8% of 160km
(b)6% of 225
Solution:
(a)  8% of 160km =$\mathrm{\frac{8}{100}&space;\,&space;of\,&space;160km&space;=\frac{8}{100}&space;\times&space;160km&space;=&space;\frac{64}{5}km&space;=&space;12.8km}$

(b)  6% of 225 = $\frac{6}{100}\times&space;225=&space;\frac{27}{2}=&space;13.50$

(vi) What % of 85 is 17  ?.
Solution :  Let x% of 85 is 17 . Then $\frac{x}{100}\times&space;85=17$

$\Rightarrow&space;85x&space;=&space;1700$
$\Rightarrow&space;x=&space;\frac{1700}{85}$

$\Rightarrow&space;x=&space;20%$

(vii) …………. % of 360 +15% of 820= 231.  Find  the missing number .
Solution :
Let the missing number be x. Then   x% of 360 +15% of 820= 231
$\Rightarrow&space;\frac{x}{100}\times&space;360&space;+&space;\frac{15}{100}\times&space;820&space;=&space;231$

$\Rightarrow&space;3.6x&space;+&space;123&space;=231$
$\Rightarrow&space;3.6&space;x=&space;231-123&space;=108$

$\Rightarrow&space;x=&space;\frac{108}{3.6}=&space;30$
Hence the missing number  is 30

(viii) (100% of ₹6) + ₹6 + (6% of ₹100) = ₹   ……..
Solution.  (100% of ₹6) + ₹6 + (6% of ₹100) =  $\frac{100}{100}\times&space;6+&space;6&space;+\frac{6}{100}\times&space;100$

= 6+6+6
=18

(ix) 50% of 50% of 1000 = ?
Solution:
50% of 50% of 1000 = $\frac{50}{100}\times&space;\frac{50}{100}\times&space;1000$
$=\frac{1}{2}\times&space;\frac{1}{2}\times&space;1000$

=250

(x) ₹3 + (100% of ₹3) + (3% of ₹100) = ?
Solution: ₹3 + (100% of ₹3) + (3% of ₹100) = $3+\frac{100}{100}\times&space;3+\frac{3}{100}\times&space;100$
= 3+3+3
=9

(xi) If 40% of 140 = x% of 200, then find the value of x .
Solution:
Given  40% of 140 = x% of 200
$\Rightarrow&space;\frac{40}{100}\times&space;140=&space;\frac{x}{100}\times&space;200$

$\Rightarrow&space;56&space;=2x$
So x= 28

(xii ) Reena deposits 60 per month in her post office saving bank account. If this is 10% of her monthly income, find her monthly income.
Solution:  Let Reena’s monthly income is  Rs. x . Then  $10&space;%&space;\,&space;\,&space;of&space;\,&space;\,&space;x&space;=60$

$\Rightarrow&space;\frac{10}{100}\times&space;x&space;=&space;60$

$\Rightarrow&space;x=&space;600$

(xiii) (8% of 35) − (35% of 8) = ?
Solution :
(8% of 35) − (35% of 8) =$\frac{8}{100}\times&space;35-\frac{35}{100}\times&space;8$

=$\frac{35\times&space;8}{100}-\frac{8\times&space;35}{100}$

= 0

(xiv) $x%&space;\,&space;of&space;\,&space;330+50&space;%\,&space;of&space;\,&space;\,&space;600=597$
Solution : $x%&space;\,&space;of&space;\,&space;330+50&space;%\,&space;of&space;\,&space;\,&space;600=597$

$\Rightarrow&space;\frac{x}{100}\times&space;330&space;+\frac{50}{100}\times&space;600&space;=597$

$\Rightarrow&space;3.3x&space;+300&space;=597$

$\Rightarrow&space;x=&space;\frac{597-300}{3.3}&space;=\frac{297}{3.3}$
$\Rightarrow&space;x=90$

(xv) If 50% of 130 = x% of 1625, then what is the value of x?
Solution:  Given  50% of 130 = x% of 1625
$\Rightarrow&space;\frac{50}{100}\times&space;130&space;=&space;\frac{x}{100}\times&space;1625$

$\Rightarrow&space;65=&space;\frac{1625x}{100}$

$\Rightarrow&space;x=\frac{65&space;\times&space;100}{1625}$

$\Rightarrow&space;x=&space;4$

## Percentage questions for Navodaya exam (Unsolved examples with answers)

1)Express each of the following as decimal :

(i)63%        (ii)      9%            (iii)     5%

2)Convert each of the following fractions into a percentage.

(ii)      $\frac{9}{25}$            (iii)   $2\frac{3}{5}$

(iii)$\frac{3}{4}$

3) 120% is equal to   ………………..

4) What % of 75 is 105 ?

5)What is the number whose 12% is 54 ?

6) Write 20m as a percentage of a km .

7)Reena deposits 60 per month in her post office saving bank account. If this is 10% of her monthly income, find her monthly income.

8)40% of (100- 20% of 300) =……….

9)Find the value of x, if 3% of x is 9.

10)90% of 300% +30% of 90 =……….

11)Find the sum whose 20% is Rs.240.

12)80% of 240 is more than 35% of 400 by………….

13)A boy gets Rs.20 per month and spends 50% of it. How much does he save in 1 yr?

14)Out of 600 students 240 are girls. What is the percentage of girls?

15)40% of 20% is equal to ……..

16)50 is what per cent of 75?

17)(100% of 5) + (5% of 100) is equal to ………..

18) Ram bought a dress worth rs. 1500 in discount and it was marked as 3800. Then how much percent he got on discount?

19) Find the number whose 15% is 24 .

20) If 5% of X + 16% of 75 = 16. Find the value of X.

Ans. 1) (i) 0.63        (ii)0.09        (iii)0.075            2)(i) 36%          (ii)260%       (iii)75%         3)1.2

4)140%             5) 450            6)2% of a km          7) Rs. 600         8) 16        9) 300        10) 297

11) 1200             12)Rs. 52       13) Rs. 120            14) 40             15)  8%      16)$\frac{200}{3}%$

17) 10

18) 50%              19) 160             20) 80