MATHEMATICS IN EVERYDAY LIFE 8

Transcription

1 MAHEMAICS IN EVEYDAY LIFE 8 Chapter 0 : Compoud Iterest ANSWE KEYS EXECISE 0.. Pricipal for st year `7600 ate of iterest 5% per aum Iterest for st year ` `80 Amout at the ed of st year ` `80 `7980 Pricipal for d year ` 7980 Iterest for d year ` `99 Amout at the ed of d year ` `99 `879 Compoud iterest Amout Pricipal `879 `7600 `779 Hece, compoud iterest `779.. Pricipal for st year `5000 ate of iterest 5% per aum Iterest for st year ` 00 `750 Amout at the ed of st year ` `750 `5750 Pricipal for d year ` Iterest for d year ` 00 `86.50 Amout at the ed of d year ` `86.50 `66.50 Compoud iterest Amout Pricipal `66.50 `5000 `6.50 Hece, compoud iterest ` Pricipal for st year `6000 ate of iterest 5% per aum Iterest for st year ` `800 Amout at the ed of st year ` `800 Pricipal for d year `6800 `6800 Iterest for d year ` `80 Amout at the ed of d year `( ) `760 Compoud iterest Amout Pricipal `( ) `60 Hece, she will pay `760 at the ed of years ad iterest is `60.. Pricipal for st year `8000 ate of iterest 8% per aum Iterest for st year ` `0 00 Amout at the ed of st year `( ) Pricipal for d year `90 ` Iterest for d year ` 00 `699.0 Amout at the ed of d year `( ) Pricipal for rd year `9.0 ` Iterest for rd year ` 00 ` Amout at the ed of rd year `( ) `.6 Mathematics I Everyday Life-8

2 Compoud iterest `( ) Compoud iterest ` Pricipal for st year `000 ate of iterest % per aum Iterest for st year ` `0 Amout at the ed of st year `( ) Pricipal for d year `0 `0 Iterest for d year ` 0 00 `.80 Amout at the ed of d year `(0 +.80) `.80 Compoud iterest Amout Pricipal `(.80 `000) ` Pricipal for st year `000 ate of iterest 9 9 % % per aum Iterest for st year ` `80 00 Amout at the ed of st year `( ) Pricipal for d year `80 ` Iterest for d year ` 00 `6.0 Amout at the ed of d year `( ) `796.0 Compoud iterest Amout Pricipal `( ) Compoud iterest ` Pricipal for st year `000 ate of iterest 0% per aum Iterest for st year ` 00 `00 Amout at the ed of st year `( ) Pricipal for d year `00 ` Iterest for d year ` 00 `0 Amout at the ed of d year `(00 + 0) `0 Pricipal for rd year `0 0 0 Iterest for rd year ` 00 ` Amout at the ed of rd year `(0 + ) `66 Hece, he will repay `66 after years. 8. Pricipal for st year `500 ate of iterest 8% per aum Iterest for st year ` `00 Amout at the ed of st year `( ) `700 Pricipal for d year `700 Iterest for d year ` `6 Amout at the ed of d year `( ) `96 Compoud iterest Amout Pricipal `(96 500) ` Pricipal for st year `500 ate of iterest 0% per aum Iterest for st year ` 00 `700 Amout at the ed of st year `( ) `00 Pricipal for d year ` Iterest for d year ` 00 `80 Amout at the ed of d year `( ) `500 Compoud iterest Amout Pricipal `( ) ` 50 Hece, compoud iterest `50. Aswer Keys

3 0. Pricipal for st year `0,000 ate of iterest % per aum 0,000 Iterest for st year ` 00 `00 Amout at the ed of st year `(0, ) Pricipal for d year `,00 `,00 00 Iterest for d year ` 00 `688 Amout at the ed of d year `( ) `5088 Hece, ahim has to pay `5088 after years. EXECISE 0.. Pricipal (P) `600, ate () 5% per aum ime () years A P 00 `600 `600 `600 ` ` ` 7056 Compoud iterest Amout Pricipal Compoud iterest ` 656 `( ). P ` 700, 6 % per aum 0 % per aum, years A P 00 ` `700 `700 `700 ` ` 5 5 `07 Compoud iterest A P `(07 700) `7. P `800, 7 % per aum 5 % per aum, year If iterest compouded semi-aually. he 5 5 half years. A P 00 `800 `800 `800 `800 `800 % per half yearly ` 8 8 `778 Hece, Aru paid `778 after oe year.. P ` 600, years, % per aum A P 00 Mathematics I Everyday Life-8

4 `600 `600 `600 ` ` 00 `7.6 Compoud iterest A P `( ) ` P `0,000, 7% p.a., years A P 00 `0,000 `0, `0, `( 07 07) `7 Hece, the amout is `7. 6. P `000, 5% p.a., years A P 00 `,000 `,000 `,000 `, ` 8 A ` Compoud iterest A P `( ) ` Compoud iterest ` P `,50,000, 8% p.a., years If iterest compouded half yearly. he, Now, we have 8 % % per half year half years A P 00 `,50,000 `,50,000 `,50, `,50, `( ) A `,8,6 Compoud iterest A P `(,8,6,50,000) `,6. 8. P ` 5,000, 5% p.a., years Simple iterest for years ` 00 `7500 Simple iterest for years `7500 P S.I. 00 Amout to be paid by avi to Shishir after two years `( ) `500 But, avi let same moey to akesh at the same rate of iterest but compouded aually for years. he, A P 00 ` Aswer Keys

5 ` 5000 ` 5000 ` A ` ` Now, gai i this trasactio 0 0 `( ) ` Hece, he gai `56.50 i this trasactio. 9. P `9000, 0% p.a., years A P 00 `9000 `9000 ` ` `(9 ) `979 Hece, Saurabh paid ` 979 after three years. 0. Let pricipal be `P. years, % p.a., S.I. `90 S.I. P 00 P `90 ` P P `8000 Now, A P 00 `8000 ` ` 8000 ` ` 5 ` Compoud iterest A P `(005.0 `8000) `05.0 Compoud iterest `05.0. P ` 5000, 0% p.a., years If iterest compouded half yearly. he, 0 % 0% per half year, half-years. A P 00 `5000 `5000 `5000 ` ` 0000 `96.50 Compoud iterest A P `( ) ` Compoud iterest ` P ` 60000, 0% p.a., years years If iterest compouded half yearly. he, 0 5% per half-year half-years Mathematics I Everyday Life-8 5

6 A P 00 `60000 `60000 `60000 ` A ` Amout ` Compoud iterest A P `( ) ` P ` 000, 0% p.a., years If iterest compouded semi-aually. he, 0 5% per semi-aually half-years A P 00 `000 `000 `000 `000 Amout ` ` 98 0 ` P `8000, % per aum If iterest compouded quarterly. he, 9 moths quarters % ( quarter moths) % per quarter A P 00 ` ` ` 8786 ` Amout ` P ` 6000, 5% p.a. for first year, 0% per aum for secod year A P `6000 `6000 ` `(80 ) ` Hece, amout to be paid for machie is ` P `8000, 0% p.a., years Whe iterest is compouded aually but time is a fractio. herefore, Amout after years `8000 `8000 ` 8000 ` ` 0 ` Aswer Keys

7 Compoud iterest A P ` `8000 Compoud iterest ` P ` 6,00,000, % 5 % per aum, year If iterest compouded half yearly. he, 5 5 % per half year half years A P 00 `6,00,000 `6,00,000 `6,00,000 `6,00,000 ` A ` 8,06, Hece, he paid ` 8,06,50 after year. 8. Let Pricipal be `P. years, 5% per aum, S.I. `800 S.I. P Now, we have P 00 S. I ` 5 P `8000 A P 00 `8000 `8000 ` `8000 `(0 ) A `880 Compoud iterest A P Compoud iterest ` `880 ` P ` 6000, 0% p.a., year If iterest compouded quarterly. he, 0 % 5% per quarter. quarters A P 00 `6000 `6000 `6000 `6000 A ` Compoud iterest `( ) ` P ` 8000, 0% p.a., years A P 00 `8000 `8000 ` A ` `590 Compoud iterest `( ) `790 If iterest compouded half-yearly. he, 0 % 0% per half year. half-year Mathematics I Everyday Life-8 7

8 8 A P 00 `8000 `8000 ` ` A ` New compoud iterest `( ) `85.80 Hece, Idu ears `( ). Let sum be `P. `.80 more moey. EXECISE 0. 5% p.a., years P P 5 S.I P S.I. 0 A P 00 5 P P 00 0 P 0 0 A P 00 Compoud iterest A P P P P C.I. S.I. P P P 0P But the differece is `60. P `60 00 P `000 Hece, the sum is ` % p.a., years For st fiace compay: S.I. S.I. P 0 P P P 00 For d fiace compay: A P 00 0 P 00 P 0 P 0 A P 000 Compoud iterest P P 000 P 000 P P + ` P P ` P 00P 000 `86 P 000 `86 P ` P `6000 Hece, the sum is ` P `8000, A `96, years,? Now, A P 00 `96 ` ` 96 ` [If a m b m, the a b] Aswer Keys

9 % p.a. 0 Hece, 5% per aum.. P `000, A `99, years,? Now, A P 00 `99 ` `99 ` % 0% per aum [If a m b m, the a b] 5. P ` 7500, A `87, years,? Now, A P 00 `87 ` ` 87 ` [If a m b m, the a b] % Hece, 6% per aum. 6. P `000, A `778, 5% p.a.? Now, A P 00 5 `778 ` ` 778 ` years [If a m a, the m ] 7. P `50, A `650, 8% p.a.? Now, A P 00 8 `650 `50 00 ` 650 ` years [If a m a, the m ] Mathematics I Everyday Life-8 9

10 8. P `000, years, C.I. `0,?, 0 A `000 + `0 `0 Now, A P 00 `0 ` `0 ` (If a m b m, the a b) % Hece, 5% per aum. 9. P `7500, years, C.I. `97,? A P + C.I. `( ) `87 Now, A P 00 `87 ` (If a m b m, the a b) % Hece, 6% per aum. 0. P ` 000, A ` 70, 5% p.a.,? Now, A P 00 5 `70 ` years (If a m a, the m ) Hece, years.. A ` 656, years, 8% p.a., P? Now, A P 00 `656 `656 `656 8 P 00 P 5 7 P P ` 7 7 P `565 Hece, the amout deposited is `565.. P `6875, % p.a., A `65856, years. Now, A P 00 `65856 ` ` ` Aswer Keys

11 years (If a m a, the m ). P ` 000, A ` 5, years years If iterest is compouded half-yearly, the half years half years A P 00 `5 ` (If a m b m, the a b) % per half yearly 0 0% per aum Hece, 0% per aum.. P `89,.5% per aum, A `, years A P 00.5 ` ` years (If a m a, the m ) 5. P `80, A `980.0, years,? A P 00 `980.0 `80 00 ` ` % 0% per aum. (If a m b m, the a b) 6. P ` 000, A ` 60.70, 6.5% p.a.,? A P `60.70 ` years (If a m a, the m ) Mathematics I Everyday Life-8

12 7. A ` 9, P? 6 % p.a. 5 % A P 00 `9 `9 `9 5 P 00 P 6 7 P P ` P ` % p.a., years Let the sum be P. S.I. Now, we have S.I. P 5 00 P P 8 00 A P 00 A 8 P 00 P 5 7 P 5 A 79 P 65 Compoud iterest A P P 5 79 P P 65 C.I. 0 P 65 Now, C.I. S.I. ` 79P 65P 65 From equatio (i) ad (ii), we get 0P P ` 65 5 p.a., years,...(i)...(ii) 0P 00P ` 65 P 65 ` 65 P ` `(8 65) `7500 he sum is ` P `60,000, A `68,69, years A P 00 `68,69 `60, `68,69 `60, % per aum. (If a m b m, the a b) 0. P ` 8000, A ` 805, 5% per aum. If iterest compouded half yearly. he, 5 % per half year A P 00 5 `805 ` `805 ` Aswer Keys

13 Hece, half years year year. A `676, P?, years, % p.a. A P 00 `676 `676 `676 `676 P P 00 P 5 6 P P ` 676 P `65 Hece, the sum is `65.. A ` 608, years, 0% per aum. A P 00 `608 `608 `608 0 P 00 P 5 6 P 5 `608 P P ` 6 P `(8 5) P `00 Hece, the sum is `00. EXECISE 0.. Preset populatio, P 0 75, 8%p.a. (icreasig), years, P? P P P 50 5 Hece, the populatio after years is 50.. ate of growth, % p.a., years Preset populatio, P 8600 Populatio years before, P 0? P P P P P P P 0 80 (approx.) Hece, populatio years ago was 80 (approx.).. Populatio of village, P 0 85 Aual birth rate 7% Aual death rate % Net growth rate (7 )% % ime, years Let P be the populatio after years. P P 0 00 P P P 85 5 P 8788 Hece, the populatio after years Mathematics I Everyday Life-8

14 . P , %, 5%, 8%, P?, years Preset populatio P P P Hece, preset populatio is per thousad 0 00% % p.a. 000 P 608, years, P 0? P P P 0 00 P P P P Hece, preset populatio is % (icrease) for first hour, 0% (decrease) for secod hour, 8% (icrease) for third hour P , Let the cout of bacteria after hours be P. P P P Hece, the cout of bacteria after hours will be P 0 `,50,000, 5% (profit) for first year, 0% (profit) for secod year P P 5 0 `,50, `,50, `,50, P `8,5,000 otal profit P P 0 `(8,5,000,50,000) `5,85, P ` 5670, 0% p.a. (decrease), years, P 0? `5670 `5670 `5670 P P P 0 00 P P P 0 ` 8 P 0 `7000 Hece before years, the price of ceilig fa was ` P 0 `7,500, 8% p.a. (depreciatio), years P P 0 00 `7,500 `7,500 `7,500 `7,500 P ` Hece after years the cost of computer will be `67.0. Aswer Keys

15 0. P `78, P 0?, 0% p.a. (depreciatio), years `78 `78 `78 P P P 0 00 P 0 5 P `78 P P 0 ` 6 P 0 `75 Hece before years, the cost of the bicycle was `75.. P 0 `,50,000, 0% per aum (depreciatio) P `,09,50,? P P `,09,50 `,50, `,09,50 `,50, years (If a m a, the m ) Hece, after years, the value of car reduced to `,09,50.. P `56, 6% p.a. (depreciatio), years, P 0? `56 `56 P P P 0 00 P 0 50 `56 7 P `56 P P 0 ` P ` Hece, before years, the value of machie was `7500. MULIPLE CHOICE QUESIONS. ate 6% per aum If iterest compouded quarterly (every three moths). he, ate 6 % per quarter Hece, optio (b) is correct.. P 0 `00, 8% p.a. (depreciatio), year, P? P P `00 00 `00 5 `00 5 P `86 he cost of electric fa after year will be `86. Hece, optio (c) is correct.. P 960, 5% p.a. (growth), years, P 0? P P P 0 00 P 0 0 P P Mathematics I Everyday Life-8 5

16 6 P P hus, the populatio before years was Hece, optio (a) is correct.. P?, P 0 65, % p.a. (depreciatio), years P P 0 00 P P 576 Preset populatio is 576. Hece, optio (d) is correct. 5. P 0 `00, P `6, years,? P P 0 00 `6 ` % 5% p.a. Hece, optio (b) is correct. (If a m b m, the a b) 6. P `000, A `, 0% per aum,? A P 00 0 ` ` years (If a m a, the m ) Hece, optio (b) is correct. 7. P `6000, % per aum 6 6 moths year If iterest compouded half yearly. he, 6% per half year half year A P 00 6 ` ` ` A `660 Hece, optio (a) is correct years If iterest compouded half yearly. he, 5 5 half years Hece, optio (c) is correct. Fill i the blaks: MENAL MAHS CONE. Compoud iterest Amout Pricipal.. Compoud iterest is calculated o the amout of the previous year. Aswer Keys

17 . Whe the iterest is compouded half yearly the give times will be twice ad the rate will be half.. here are 0 quarters i years. 5 years 5 quarters 5 quarters 0 quarters ( year quarters) 5. he relative decrease i the value of a item over a period of time is called depreciatio. EVIEW EXECISE. P `0000, 6% p.a., year If iterest compouded half yearly. he, 6 % per half year half years A P 00 A `0,000 `0,000 `0,000 A ` Hece, he will get `8 after year.. Let Pricipal be `P. Simple iterest (S.I.) Ad, years, 0% p.a. S.I. P 00 P 0 P 00 0 A P 00 A 0 P 00 P 0 P P Compoud iterest (C.I.) A P P P 000 C.I. P 000 C.I. S.I. `9 P P P 00P 000 P 000 P 000P 000 `9 `9 ` P ` P ` 000 Hece, pricipal is `000.. P `000, C.I. `0, years A P + C.I. `( ) A `0 A P 00 `0 ` `0 ` (If a m b m, the m ) Hece, 5% per aum. Mathematics I Everyday Life-8 7

18 . P `600, A `85.0, 5% p.a.,? 8 ` 85.0 ` 600 A P years. (If a m a, the m ) 5. P 0 `0000, 5% p.a. (depreciatio) years, P? P P P ` `0000 P `0000 ` ` 6 P `656.5 Hece, the cost of a.v. set after years will be ` P `000, 5% p.a., A `0, years A P 00 5 `0 ` Hece, years. (If a m a, the m ) 7. P ` 00, A ` 576, 8% p.a.,? If iterest compouded half yearly. he 8 % % per half yearly A P 00 ` 576 ` Let the sum be `P half year 6 moths A `986, years, 5 % p.a. If iterest compouded half yearly. he, 5 half years, A P 00 `986 `986 ` 986 ` % per half year 5 P 00 5 P 00 P 80 8 P 80 Hece, sum is ` P ` 8000, 0% p.a., P ` P ` moths 9 year year Aswer Keys

19 If iterest compouded quarterly. he, 0 % 5% per quarter quarters quarters A P 00 5 ` ` ` ` A ` 96 Compoud iterest A P `( ) `6 0. P 75760, 0 per thousad per aum % 000 % per aum, years P P 0 00 P 0 00 P P P P P Hece, three years ago, the populatio of a two was HOS QUESIONS. P 0 `,75,000, 0% p.a., years P P `,75, `,75,000 5 `,75,000 `,75,000 P `89, otal depreciatio i the price of the car `,75,000 `89,600 `85,00.. P `5000, 0% p.a., years, C.I. `655 A P + C.I. `( ) `6655 A P 00 0 `6655 ` years. Let the sum be `P. 5%, years A P 00 A 5 P 00 A P 0 A 59 P 00 C.I. A P `90 59 P P 00 59P 00P `90 00 `90 9 P P ` 9 P `000 Hece, I had borrowed `000. (If a m a, the m ) P 0 Mathematics I Everyday Life-8 9

20 Let us cosider 5 studets stadig at the vertices of a 5-sided polygo as show i the figure. We ca represet shakig hads by a studet (say ) to rest of the studets by drawig lies from the vertex to the other vertices We see that, there are (5 ) such lies, i.e., studet has to shake hads times. hus, each vertex requires lies to joi to every other vertices. here are total 5 lies of joiig. But each of these lies has bee couted (draw) twice, oce from each vertex. hus, total umber of lies joiig every vertex to every other vertices i.e., total umber of hadshakes Aswer Keys