Job Maths Preparation: Percentage

Percentage

শতকরা বিষয়ক অংক চাকরির পরীক্ষার জন্য খুবই গুরুত্বপূর্ণ। ত্রিশটি অংকের মধ্যে ৪ থেকে ৬টি অংশ পারসেনটেজ দিয়ে করা যায়। তাছাড়া ঐকিক নিয়ম, লাভ ক্ষতি, সুদকষা সবই মূলত পারসেনটেজ হিসেব করে করা হয়। তাই একথা বলা যায় যে পারসেনটেজ হিসেব দ্রুত না করতে পারলে পাটিগণিত অংক আপনি দ্রুত করতে পারবেন না। নিচের সমস্যাগুলো বোঝার চেষ্টা করুন। প্রদত্ত সমস্যাগুলো দ্রুত হিসেব করতে শিখুন।

Convert each of the following fractions as percentage :

♣ 3/25 = (3/25 × 100) % = 12 %

♣ 4/5 = (4/5 × 100) % = 80 %

♣ 3/4 = (3/4 × 100) % = 75 %

♣ 2/3 = (2/3 × 100) % = (200/3) % = 66 %

♣ 1 = (1 × 100) % = 100 %

বিষয়টা বুঝতে পারলে এরকম হিসেবগুলো দেখেই বলে দেওয়া সম্ভব। এগুলো জানা থাকলে পরীক্ষায় অংক করার গতি অনেক বেড়ে যাবে।

 

Express each of the following fractions into a percentage :

♣ 6/5 = (6/5 × 100) % = 120 %

♣ 5/4 = (5/4 × 100) % = 125 %

♣ 22/5 = (22/5 × 100) % = 440 %

পার্সেন্টেজ মানে ১০০-এর হিসেবে সব সময় কম হবে এমন নয়, এটি বেশিও হতে পারে।

 

Express each of the following percentage into fraction in lowest terms :

♣ 16 % = 16/100 = 4/25

♣ 48 % = 48/100 = 12/25

♣ 5 % = 5/100 = 1/20

♣ 25 % = 25/100 = 1/4

♣ 115 % = 115/100 = 23/20

♣ 1 % = 1/100

♣ 24 % = 24/100 = 6/25

♣ 62 % = 62/100 = 31/50

♣ 30 % = 30/100 = 3/10

♣ 75 % = 75/100 = ¾

♣ 10 % = 10/100 = 1/10

 

Convert each of the decimal percentage as fractions in the lowest form

♣ 3.5 % = 35/10 % = 35/10 × 1/100 = 7/100

♣ 0.5 % = 5/10 % = 5/10 × 1/100 = 1/200

♣ 30.2% = 322/10 % = 322/10 × 1/100 = 322/1000 = 151/500

♣ 0.4 % = 4/10 % = 4/10 × 1/100 = 4/1000 = 1/250

♣ 0.375 % = 375/1000 % = 375/1000 × 1/100 = 375/100000 = 3/800

 

Convert each of the fraction percentage as fractions in the lowest form :

♣ 17/5 % = 17/5 × 1/100 = 17/500

♣ 2/5 % = 2/5 × 1/100 = 1/250

♣ 50/3 % = 50/3 × 1/100 = 50/300 = 1/6

♣ 41/8 % = 41/8 × 1/100 = 41/800

♣  2¾ % = 11/4 % = 11/4 × 1/100 = 11/400

১০০ নিচে গুণ হয়েছে তারপর সরল করা হয়েছে।

 

Express each of the following percentage as ratios in the simplest form :

♣ 46 % = 46/100 = 23/50 = 23 : 50

♣ 20 % = 20/100 = 1/5 = 1 : 5

♣ 125 % = 125/100 = 5/4 = 5 : 4

♣ 34% = 34/100 = 17/50= 17 : 50

♣ 1 % = 1/100 = 1 : 100

 

Express each of the following fraction percentage into ratio in lowest term:

♣ 3/4 % = 3/4 × 1/100 = 3/400 = 3 : 400

♣ 62/3 % = 20/3 % = 20/3 × 1/100 = 20/300 = 1 : 15

♣ 3/5 % = 3/5 × 1/100 = 3/500 = 3 : 500

♣ 62/5 % = 32/5 % = 32/5 × 1/100 = 32/500 = 8/125 = 8 : 125

♣ 3/8 % = 43/8 % = 43/8 × 1/100 = 43/800 = 43 : 800

 

Express each of the following decimal percentage as ratios in the simplest form:

♣ 16.5 % = 165/10 % = 165/10 × 1/100 = 165/1000 = 33/200 = 33 : 200

♣ 0.4 % = 4/10 % = 4/10 × 1/100 = 4/1000 = 1/250 = 1 : 250

♣ 2.5 % = 25/10 % = 25/10 × 1/100 = 25/1000 = 1/40 = 1 : 40

♣ 10.10 % = 1010/100 % = 1010/100 × 1/100 = 1010/10000 = 101/1000 = 101 : 1000

♣ 1.2 % = 12/10 % = 12/10 × 1/100 = 3/250 = 3 : 250

 

Express each of the following ratio into percentage:

♣ 6 : 5 = 6/5 = (6/5 × 100) % = 600/5 % = 120 %

♣ 8 : 25 = 8/25 = (8/25 × 100) % = 32 %

♣ 10 : 50 = 10/50 = (1/5 × 100) % = 20 %

♣ 4 : 5 = 4/5 = (4/5 × 100) % = 80 %

♣ 7 : 25 = 7/25 = (7/25 × 100) % = 28 %

 

Convert each of the following ratios as fraction percentage:

♣ 20 : 70 = 20/70 = (20/70  × 100) %  = 2000/70 % = 200/7 %

♣ 17 : 24 = 17/24 =  (17/24 × 100) %  = 1700/24 % = 425/6 %

♣ 128 : 175 = 128/175 = (128/175 × 100) % = 512/7 %

♣ 2 : 3 = 2/3 = (2/3 × 100) % = 200/3 %

♣ 1 : 15 = 1/15 = (1/15 × 100) % = 100/15 % = 20/3 %

 

Convert each of the following ratios into decimal percent:

♣ 1 : 8 = 1/8 = (1/8 × 100) % = 100/8 % = 12.5 %

♣ 30 : 80 = 30/80 = (30/80 × 100) % = 3000/80 % = 75/2 % = 37.5 %

♣ 5 : 8 = 5/8 = (5/8 × 100) % = 500/8 % = 125/2 % = 62.5 %

♣ 11 : 16 = 11/16 = (11/16 × 100) % = 1100/16 % = 275/4 % = 68.75 %

♣ 8 : 125 = 8/125 = (8/125 × 100) % = 800/125 % = 32/5 % =  6.4 %

 

Express each of the following percentage as decimals:

♣ 23 % = 23/100 = 0.23

♣ 16 % = 16/100 = 0.16

♣ 47 % = 47/100 = 0.47

♣ 1 % = 1/100 = 0.01

♣ 25 % = 25/100 = 0.25

 Note: Decimal shifts by 2 places to the left.

 

Express each of the following decimal percentage as decimals:

♣ 1.75 % = 1.75/100 = (1.75 × 100)/(100 × 100) = 175/10000 =  0.0175

♣ 7.5 % = 7.5/100 = (7.5 × 10)/(100 × 10) = 75/1000 = 0.075

♣ 31.5 % = 31.5/100 = (31.5 × 10)/(100 × 10) = 315/1000 = 0.315

♣ 0.18 % = 0.18/100 = (0.18 × 100)/(100 × 100) = 18/10000 = 0.0018

♣ 231.2 % = 231.2/100 = (231.2 × 10)/(100 × 10) = 2312/1000 = 2.312

Note: Decimal shifts by 2 places to the left.

 

Express each of the following fraction percentage as decimals:

♣ 4/5 % = 0.8 % = 0.8/100 = (0.8 × 10)/(100 × 10) = 8/1000 = 0.008

♣ 9/20 % = 0.45 % = 0.45/100 = (0.45 × 100)/(100 × 100)

= 45/10000 = 0.0045

♣ 1/80 % = 0.0125 % = 0.0125/100  = (0.0125 × 10000)/(100 × 10000) = 125/1000000 = 0.000125

♣ 13/50 % = 0.26 % = 0.26/100 = (0.26 × 100)/(100 × 100) =   26/10000 = 0.0026

♣ 44/5 % = 8.8 % = 8.8/100 = (8.8 × 10)/(100 × 10) = 88/1000 = 0.088

 

Express each of the following decimal as percent:

♣ 0.8 = 0.8 × 100 % = 80 %

♣ 1.2 = 1.2 × 100 % = 120 %

♣ 7.1 =  7.1 × 100 % = 710 %

♣ 10.1 = 10.1 × 100 % = 1010 %

♣ 31.3 = 31.3 × 100 % = 3130 %

♣ 123.7 = 123.7 × 100 % = 12370 %

♣ 101.9 = 101.9 × 100 % = 10190 %

Note : Decimals shifts by 2 places to the right.

 

Express each of the following statements in the percentage form:

♣ 5 out of 20 are bad = 5/20 eggs are bad = (5/20 × 100) % eggs are bad = 25 % eggs are bad

♣ 3 children in a class of 30 are absent = 3/30 children are absent

= (3/30 × 100) % children are absent

= 10 % children are absent

♣ 21 apples out of 30 are good = 21/30 apples are good

= (21/30 × 100) % apples are good

= 70 % apples are good

♣ 47 students out of 50 are present = 47/50 students are present

= (47/50 × 100) % students are present = 94 % students are present

 

Percentage of the given Quantity

1. Find 40 % of 24      

Solution : We know that R % of m is equal to R/100 × m.

So, we have 40 % of 240 Or, 40/100 × 240 = 96

2. 10 % of 1 hour

Solution : We know that R % of m is equal to R/100 × m.

So, we have 10 % of 1 hour.

10 % of 60 minutes (Since, 1 hour = 60 minutes)

= 10/100 × 60 minutes = 6 minutes

3. Find 15 % of $250

Solution : We know that R % of m is equal to R/100 × m.

So, we have 15 % of $250. 15/100 × 250 = $75/2 = $37.5

4. Find 120 % of 25 km

Solution : 120 % of 25 km = (120/100 × 25) km = 30 km

5. Find 10 % of 400 kg

Solution : 10 % of 400 kg = (10/100 × 400) kg = 40 kg

6. Find the number whose 8 % is 72.

Solution : Let, the required number be m, then

8 % of m = 72 ⇒ 8/100 × m = 72 ⇒ m = 72 × 100/8 ⇒ m = 900

Therefore, the required number is 900.

7. Express each of the following as a fraction:

i.64 %                   ii. 6%                    iii. 0.5%.

Solution : i. 64% = =         ii. 6 % = =                        iii. 0.5 % = = =

8. Express each of the following as a decimal :

i.36 %                   ii. 8%                    iii. 0.3 %

Solution :  i. 36 % = 36/100 = 0.36.   ii. 8% = 8/100 = 0.08.         iii. 0.3 % = 0.3/100  = 0.003.

9. Express the following as rate per cent:

i. 0.1               ii. 29                      iii. 0.002

Solution : 0.002 = 0.002 * 100% = 0.2%.

10. Find the percent :

i. 70% of 70         ii. 90% of 9         iii. 3 % of 6

Solution  : i. 70 % of 70 = 49  ii. 90% of 9 = 8.1 iii. 3 % of 6 = 0.18

 

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