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and :, Downloaded from https:// www.studiestoday.com, • Speed, Distance and Time, • Percentage and its Applications, TAURatio and Proportion ĐAT Time and Work, UNIT, THREE, gnie, Commercial Arithmetic, Let's Recap, noitbubonl, l gnidsiow, 1. Divide the following in the given ratios., (i) Rs 1584 in a 5:7 ratio, (ii) 3 kg 696 g in a 9: 12 ratio, (iii) 7 € 896 ml in a 11: 13 ratio, (iv) 42 km 107 m in a 20 : 21 ratio, (v) 1h 54 min 8 s in a 15: 17 ratio, 2. Find the value of x if the following ratios are in direct proportion., (i) 27 : 189 and 31 : x, To, oilA, lo, (ii) 41 : 20.5 and x: 32, 5 1, (iii) 2.55 : x and 3.6: 5.04, (iv) 18 6, 3. 5 gardeners can weed a garden in 3 days. How long will 3 gardeners take to weed the same garden?, 4. A man 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, That means our club earns 50 p every time, 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, someone visits the site. Imagine, if even 0.1%, of all web surfers visit our site, how much, Great news! A big company, has agreed to sponsor our, club's website., money would it lead to? This is when we talk, about millions of web surfers!, evia, 26, di, 87, Downloaded from https://www.studiestoday.com

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Downloaded from https:// www.studiestoday.com, 11, PERCENTAGE AND ITS APPLICATIONS, THRE, Simple Interest, Compound Interest, Percentage of a Given Measure, Profit and Loss, Discount, A Introduction, Example 2: 24% of a block of ice weighing 4 kg, 350 g melted away. What is the weight of ice now?, 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., Method I, 24% of 4.35 kg, Common Fraction, Decimal, Per cent, Percentage, 24, 104.4, x 4.35 =, 100, %3D, 100, 3., 75, 1.044 kg, Remaining ice = 4.35 - 1.044, = 3.306 kg, = 3 kg 306 g, 0.75, 75%, %3D, 4, 100, 12, 48, 0.48, 48%, 25, 100, %3D, ,7, 187.5, 1.875, 187.5%, 8, 100, Method II, 1. To convert a fraction into percentage, multiply the, given fraction by 100 and write the symbol %' after, the product., 2. To convert a decimal into percentage, shift the decimal, point by two places to the right and write the symbol, "% after the result., Melted percentage of ice 24%, Remaining percentage of ice =, Hence, 76% of 4.35 kg, = 3.306 kg, 3 kg 306 g, 100-24 76%, %3D, or, Expressing numbers in percentages is a very, common method used in the comparison of mea-, Measure as a Percentage of Another, Measure, sures. 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, Example 3: 7e 524 ml of an 8l 550 ml solution is, water. Express it in percentage., appear for., Measure as percentage of another measure, First measure, Percentage of a Given, A Measure, x 100%, %3D, Second measure, 7.524, x 100%, %3D, 8.550, Example 1: What is 41% of 7 kg?, = 88%, 41, 41% of 7 kg, 287, kg, x 7 kg =, %3D, 100, 100, Thus, 78 524 ml of water is 88% of the 8 550 ml, = 2.87 kg or 2 kg 870 g, solution., %3D, 88, 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, 40, of money received = Rs 558, 100, %3D, or, entrance examination, only 294 passed. What, was the percentage of failures in that examination?, 558x100, Money received:, = Rs 1395.00, 40, Number of failures = 8400 - 294 = 8106, %3D, %3D, Now money received = 5% of father's salary, 8106, Percentage of failures, x 100%, %3D, Rs 1395 =, of father's salary, 100, 8400, or, 96.5%, %3D, 1395 x100, Father's salary =, = Rs 27900.00, %3D, Try this!, 1. Express 56% as a fraction., Example 6: 50% of the people in a restaurant are, tea drinkers, 35 re coffee drinkersvhile 20%, drink com, as well as tea. If cople drink coffee, people, .ell as tea, how m, the restaurant, 2. Express 02% as a decimal., drink neither co nor tea?, Let us use a Venn diagram to help us solve this, problem., Percentage of people who drink tea, but not coffee, A Word Problems, 50% - 20% = 30%, %3D, Percentage of people who drink coffee, but not tea, = 35% - 20% = 15%, 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, %3D, Thus, people who drink either tea or coffee, = 30% + 20% + 15% = 65%, %3D, Thus, people who drink neither tea nor coffee, = 100% - 65% = 35%, much does Prachee's father earn?, She saves 60%. She, 35%, spends remaining 40%., Out of 40%, she spends, 50%, 25% on a doll., Number of people who drink both coffee and, tea = 8, Given, 20% of total people = 8, 25% of money spent = Rs 139.50, 20, of total people = 8, %3D, or, 25, 100, of money spent = Rs 139.50, 100, 8x100, = 40, %3D, = Total people in the restaurant =, 20, %D, 139.50x100, = Rs 558, Number of people who drink neither tea nor coffee, = 35% of 40 people, Money spent, %3D, 25, Now, money spent, (100% - 60%) of money, %3D, received, 35, x 40 people, 100, %3D, Rs 558 = 40% of money received, from her father, or, = 14 people, 89, Downloaded from https://www.studiestoday.com

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Downloaded from https:// www.studiestoday.com, Thus, net fall in price of onions 0 slqumaxa, TndW boeanq = 100-93.75 = Rs 6.25 s, Soonenim le ni lis, Thus, net fall percentage, Example 7: 10% of a cold drink is orange con-, centrate while the rest is w ter. If there is 304 ml, %3D, more of water than orange concentrate, find the, volume of the cold drink., 6.25, x 100%, 2a100 lo 15emu, %3D, When 10% o. tal volume i orange concentrate,, then 90% of t ta volume is rater., a018, = 6.25%, 70, 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?, Difference n percenta, of water and orange, = 90%- 10 = 80%, concentra, Difference in volme of water and orange, concentrate = 30 ml, Thus 80% of total volume of cold drink o nnb, 304 ml, wod t as lon s, 304 x 100 b, If one could buy 100 candles for Rs 100 last year,, then one can buy 100 candles for Rs 150 this year., %3D, Total volume of cold drink =, %3D, 100, 80, So this year one can buy, 150, candles for Re 1., = 380 ml, 3, 2, nsllong This implies Mrs Diwan can buy, x 100 = 662, 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?, 3., candles for Rs 100 this year.o19 bioW, 2, Thus, reduction of purchases = 100 – 66=, %3D, 2ovee sd bdrid od, Thus, reduction percentage, wod 0.0 reduction, b 33 candles, Let the price of onions before any price change, niyh ode, be Rs 100., After price rise of 25%, price of onions, x 100% = 33-%, 3bum, %3D, %3D, olloo son = 100 + 25% of 100 = Rs 125T, previous purchase, %3D, After price fall of 25%, price of onions, = 125 - 25% of 125, = 125 – 31.25 Rs 93.75, 1,, Mrs Diwan has to buy 33-% less candles this year, 3, in order to spend the same amount as last year., Exercise 11.1, olgoog lo odmn, 1. Express the following in percentage., 7., 2. Express the following decimals in percentage., (i) 0.6, (iii) 1.53, (v) 1.3005, (vii) 1 0.e8, (ix) 0.0001, 3. Express the following percentages in fractions, (ii) 0.65, (iv) 0.027, (vi) 0.99, (viii) 0.218, (x) 0.01 -, (1) beobe, 20, (i), evi, (ii), (iv), 25, 35 leoT=, (vi), 40 lod, 66, (v), 80, drion, 10 beobye, (viii), 57, 19, as well as decimals., (ii) 45%, (iv) 16%, oi (vi) 55%, (vi), 75, (i) 40%, (iii) 88%, (v) 38%, bovis, 25, m beobye, 21, (ix), 40, (x), 50, 90, Downloaded from https://www.studiestoday.com

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Downloaded from https://www.studiestoday.com, 14. The price of potatoes first increased by 10%, dal and then fell by 8%. Find the net percentage, change in the price of potatoes.itgiow, 15. 46% of all attending a school assembly are girls,, g52% are boys, and the rest are teachers. If there, are 598 boys in the school assembly, how many, 1 teachers are there?, meni 000 w agelliv, (vii) 124%, lugoq, noitg d, (ix) 62.5%, .2,, (viii) 66 %, 3, (x) 83-%, 3, 4. What percentage is:, (i) 474 m of 1 km 896 m?, cin, aue boesoni, adr i) 124 of 80?, (iii) 4 e 750 ml of 38 ?, (iv) 26 m of 3 km 250 m?, (v) 2127 graduates of 14180 people?, lles, 5. How much is:, i) 45% of 180 people?, (ii) 3% of 150 g?, (iii) 95% of 4 kg 560 g?, (iv) 60% of 3 l 905 ml?, (v) 52% of 94? 0010, 6. Mr Lal was earning Rs 14,950 per month when, he was given a salary increment of Rs 971.75., What was the percentage rise in Mr Lal's salary?, 7. A restaurant sold 1560 bottles of cold drinks in, i July 2009, but only 858 bottles in August 2009., gWhat was the percentage fall in the sale of cold, Ti ldrinks?nq adw ta ilenq, 8. 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?, 9. 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?, 10. A worker receives Rs 11,250 as bonus which, works out to l15% of his annual salary. What is, his monthly salary?, 11. A man goes to a gym and loses 8% weight. If, P his weight loss was 6 kg 560 g, find how much, bas he weighed earlier., 12. 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?, 13. If 60% of the population of a village is 924, se villagers, how many villagers will be 25% of, the population?, Alo, To sbam, no haial, on, dw shanra, 16. In a combined 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, Si gnims, for the test?, 17. 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?, 18. If Atul is 20% taller than Ajay, by what, percentage is Ajay shorter than Atul?, 19. 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?, 20. 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?, 21. A sum of money was distributed between A and, oB such that A got 60% of all the money. If B, got Rs 1170 less than A, how much money was, 001, distributed between A and B?, 22. 53% of the weight of a concrete slab is cement, while the rest is stone and sand. If there is, 91, Downloaded from https:// www.studiestoday.com