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Downloaded from https:// www.studiestoday.com, , , , , , ° Percentage and its Applications ° Speed, Distance and Time, e Ratio and Proportion e Time and Work, , Let’s Recap, , 1, Divide the following in the given ratios., (i) Rs 1584 ina 5: 7 ratio, (ii) 3kg 696 gin a9: 12 ratio, (iii) 7 2896 mé ina 11 : 13 ratio, (iv) 42 km 107 m ina 20: 21 ratio, (v) 1h 54min 8 sina 15: 17 ratio, 9. Find the value of x if the following ratios are in direct proportion., (i) 27: 189 and 31: x (Gi) 41 : 20.5 and x: 32, |, |, , , , Srl 1, eee ‘ > . eS. : ae 1l— a, (iii) 2.55 : x and 3.6 : 5.04 (iv) 1386 and 46, , 3. 5 gardeners can weed a garden in 3 days. How long will 3 gardeners take to weed the same garden?, 4. Aman buys a 14” TV for Rs 4176 from an electronics shop advertising a 20% discount. If the marked, price of the TV was 45% above its cost price, how much had the shop bought the TV for?, , , , , , , , , , , , , , , , , , , , , , , Don't count your chickens before they are, hatched! We'll have to do a bit of arithmetic, before we actually start, like placing text and, , pictures proportionately in a page, deciding as, , to what percentage of the page should have the, sponsor's advertisement, etc. This would involve, a lot of work and we've very little time, , =, , , , , , , , , , That means our club earns 50 p every time, someone visits the site. Imagine, if even 0.1%, of all web surfers visit our site, how much, money would it lead to? This is when we talk, , about millions of web surfers!, ’ ———, , , , , , , , , , Great news! A big company, has agreed fo sponsor our, , club's website., , , , , , , , , , , , , Downloaded from https:// www.studiestoday.com

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Downloaded from https:// www.studiestoday.com, , 11, , PERCENTAGE AND ITS APPLICATIONS, , , , * Discount, , A Introduction, , A fraction is a part of a whole, a decimal is a part of, a power of 10, and a per cent is a part of 100., , , , , , Common Fraction Decimal Per cent Percentage, 4 0.75 100 75%, 12 48 4, 95 0.48 100 48%, a 187.5 f, 3 1.875 100 187.5%, , , , , , 1. ‘To convert a fraction into percentage, multiply the, given fraction by 100 and write the symbol ‘%’ after, the product., , 2. Toconvert a decimal into percentage, shift the decimal —, point by two places to the right and write the symbol, ‘%’ after the result. ;, , , , , , , , Expressing numbers in percentages is a very, common method used in the comparison of measures. By now it must have become a common word, in your vocabulary, as you must be using it to, compare the marks scored in all the tests you, appear for., , Percentage of a Given, Measure, , , , Example 1: What is 41% of 7 kg?, , 41 287, 41% of 7kg = —~ X7kg= —~ ke, , 100 100, , = 2.87 kg or 2 kg 870 g, , , , Example 2: 24% of a block of ice weighing 4 kg, , 350 g melted away. What is the weight of ice now?, , Method I, 24% of 4.35 kg, 24, Tepes ST, = 1.044 kg, Remaining ice = 4.35 — 1.044, = 3.306 kg, = 3kg 306 ¢, , _ 104.4, , Method IT, , Melted percentage of ice = 24%, Remaining percentage of ice = 100 — 24 = 76%, Hence, 76% of 4.35 kg, = 3.306 kg, or 3 kg 306 g, , Measure as a Percentage of Another, Measure, , Example 3: 7¢ 524 mé of an 8£ 550 m£ solution is, water. Express it in percentage., , Measure as percentage of another measure, First measure, , —~ Second measure x 100%, , 7 oad, , 8.550, = 88%, , Thus, 7 524 mé of water is 88% of the 8 £550 mé, solution. ;, , , , x 100%, , Downloaded from https:// www.studiestoday.com

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Downloaded from https:// www.studiestoday.com, , Example 4: Out of 8400 candidates who sat for an, entrance examination, only 294 passed. What, was the percentage of failures in that examination?, , Number of failures = 8400 — 294 = 8106, , 81, P i sig 9, ercentage of failures 8400 x 100%, , = 96.5%, , awe dedmutond, :, , Pee ep at, , mht, as ity press 56% as a fraction., , ht tat, app} eit, t ; ;, , sd 2. Express 02% as a decimal., , A Word Problems, , Example 5: Prachi’s father gives her 5% of his, monthly salary to spend on her birthday. She saves, 60% of the money given to her and spends 25% of, the rest on a doll. If the doll costs Rs 139.50, how, , much does Prachee’s father earn?, , , , , , 25% of money spent = Rs 139.50, , , , weN, => 00 of money spent = Rs 139.50, 139.50 x 100, => Money spent = 95 = Rs 558, Now, money spent = (100% —60%) of money, received, , oe. Rs 558 = 40% of money received, > from her father, , 40, , or 100 of money received = Rs 558, , “ 558 x 100, => Money received = orn Rs 1395.00, Now money received = 5% of father’s salary, , 5, or Rs 1395 = 100 of father’s salary, 1395 x 100, , = Father’s salary = = Rs 27900.00, , Example 6: 50% of the people in a restaurant are, tea drinkers, 35% are coffee drinkers while 20%, drink coffee as well as tea. If 8 people drink coffee, as well as tea, how many people in the restaurant, drink neither coffee nor tea?, , Let us use a Venn diagram to help us solve this, , problem., , Percentage of people who drink tea, but not coffee, = 50% — 20% = 30%, , Percentage of people who drink coffee, but not tea, = 35% — 20% = 15%, , Thus, people who drink either tea or coffee, = 30% + 20% + 15% = 65%, , Thus, people who drink neither tea nor coffee, = 100% —65% = 35%, , , , T, , Cc, "C6 ts, , Number of people who drink both coffee and, tea = 8, , , , , , , , , , Given 20% of total people = 8, a f total le =8, or 100 ol total people =, 8x 100, = Total people in the restaurant = “5 = 40, , Number of people who drink neither tea nor coffee, = 35% of 40 people, 35, , = 700 x 40 people, , = 14 people, , a, , Downloaded from https:// www.studiestoday.com

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Downloaded from https:// www.studiestoday.com, , Example 7: 10% of a cold drink is orange concentrate while the rest is water. If there is 304 mé, , more of water than orange concentrate, find the, volume of the cold drink., , When 10% of total volume is orange concentrate,, then 90% of total volume is water., , Difference in percentage of water and orange, concentrate = 90% — 10% = 80%, , Difference in volume of water and orange, concentrate = 304 mf, , Thus 80% of total volume of cold drink, = 304 m2, 304 x 100, , = Total volume of cold drink = 80, , = 380 m2, , Example 8: The price of onions rises 25% and then, falls 25%. What is the net rise or fall per cent in the, price of onions?, , Let the price of onions before any price change, be Rs 100., After price rise of 25%, price of onions, = 100 + 25% of 100 = Rs 125, After price fall of 25%, price of onions, = 125 25% sof 125, =.125=3125'=,Rs 93.75, , Exercise 11.1, , 1. Express the following in percentage., , ak pa, , @ 5 @) 5, , oe 101g, (ii) 3 (iv) 95, 66 OS, , ) $0 1) Zo, ae ce 9, , (vii) 75 (viii) 95, l ou, , (ix) aij (x) 0, , Thus, net fall in price of onions, = 100-— 93.75 = Rs 6.25, , 6.25, Thus, net fall percentage = 700. x 100%, , = 6.25%, , Example 9: Mrs Diwan spends a fixed amount, every Diwali for buying candles. If the price of, candles has gone up by 50% this year and, Mrs Diwan still insists on spending the same amount, as last year, by how much percentage must, Mrs Diwan reduce her purchase of candles?, , If one could buy 100 candles for Rs 100 last year,, , then one can buy 100 candles for Rs 150 this year., , 100 2, So this year one can buy tees candles for Re 1., , 2 2, This implies Mrs Diwan can buy ae 100 = er, , candles for Rs 100 this year., , vs, Thus, reduction of purchases = 100 — oS, , = 331 candles, 3, , Thus, reduction percentage, , reduction 9g l 7, Sn ee 0 — —, ~ previous purchase * an 3°, , ; l, Mrs Diwan has to buy poo less candles this year, , in order to spend the same amount as last year., , 2. Express the following decimals in percentage., , (i) 0.6 (ii) 0.65, , (ii) 1.53 (iv) 0.027, (v) 1.3005 (vi) 0.99, (vii) 1 (viii) 0.218, (ix) 0.0001 (x) 0.01 , 3. Express the following percentages in fractions, as well as decimals., , (i) 40% (li) 45%, (iii) 88% (iv) 16%, (v) 38% (v1) 55%, , Downloaded from https:// www.studiestoday.com

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(wii) 124%, , 4,, , 10., , ae, , 12., , Downloaded from https:// www.studiestoday.com, , (viii) 66=%, (ix) 62.5% (x) 835%, , What percentage is:, (i) 474 m of 1 km 896 m?, (ii) 124 of 80?, (iii) 4 2 750 mé of 38 £?, (iv) 26 m of 3 km 250 m?, (v) 2127 graduates of 14180 people?, , . How much 1s:, , (i) 45% of 180 people?, (ii) 3% of 150 g?, (iii) 95% of 4 kg 560 g?, (iv) 60% of 3 £905 mé?, (v) 52% of 94?, Mr Lal was earning Rs 14,950 per month when, he was given a salary increment of Rs 971.79., What was the percentage rise in Mr Lal’s salary?, , _ A restaurant sold 1560 bottles of cold drinks in, , July 2009, but only 858 bottles in August 2009., What was the percentage fall in the sale of cold, drinks?, , . Pooja receives Rs 275 as pocket money and, , spends 30% on books, 35% on toys, 15% on, chocolates, and saves the rest. How much money, does Pooja save?, , The price of petrol was Rs 42.50. The price, was first increased by 4% and then reduced by, 5%. What is the price of petrol now?, , A worker receives Rs 11,250 as bonus which, works out to 15% of his annual salary. What is, his monthly salary?, , A man goes to a gym and loses 8% weight. If, his weight loss was 6 kg 560 g, find how much, he weighed earlier., , 65% of all the fruits in a shop, at the beginning, of the day, were apples. After selling 75% of all, apples there were 104 apples left at the end of, the day. How many fruits were in the shop to, , ~ begin with?, i., _ villagers, how many villagers will be 25% of, , If 60% of the population of a village is 924, , the population?, , 14., , 15., , 16., , We, , 18., , Is., , 20., , rae, , 22., , The price of potatoes first increased by 10%, and then fell by 8%. Find the net percentage, change in the price of potatoes., , 46% of all attending a school assembly are girls,, 52% are boys, and the rest are teachers. If there, are 598 boys in the school assembly, how many, teachers are there?, , , , , , In acombined test on Maths and Science, 7.5%, failed in Maths, 22.5% failed in Science, and, 5% failed in both the subjects. If 120 students, passed in both subjects, how many students sat, for the test?, , The water level in a tank rises 20% when it is, filled in the morning and then falls 20% during, the day. What is the net rise or fall in the water, level in the tank?, , If Atul is 20% taller than Ajay, by what, percentage is Ajay shorter than Atul?, , Amir goes to a gym and loses 10% of his weight., His mother thinks he looks too skinny now. By, how much percentage must Amir gain weight, to return to his previous weight?, , The bushes in a hedge have grown 25% in, height. What percentage of their current height, needs to be trimmed off to return them to their, former height?, , Asum of money was distributed between A and, B such that A got 60% of all the money. If B, got Rs 1170 less than A, how much money was, distributed between A and B?, , 53% of the weight of a concrete slab is cement, while the rest is stone and sand. If there is, , a, , Downloaded from https:// www.studiestoday.com