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Chapter : 8 Comparing quantities Exercise : 8.1 q.1: Find ratio of the following : (a): Speed of a cycle 15 km per hour to the speed of scooter 30 km per hour . Sol : Ratio = 15 km : 30 km = 15 : 30 = 15/30 = 1/2 =1:2 (b) : 5 m to 10 km . Sol : Ratio = 5 m : 10 km = 5 m : 10000 m = 5 : 10000 = 5/10000 = 1/2000 = 1 : 2000 (c) : 50 paise to Rs 5 . Sol : Ratio = 50 paise : Rs 5 = 50 paise : 500 paise = 50 : 500 = 50/500 = 1/10 = 1: 10 Q.2 : Convert the following ratio to % : (a) : 3 : 4 Sol : 3 : 4 % = 3/4 = 3/4 x 100 = 75 % 2:3 (b) : Sol : 2 : 3 % = 2/3 = 2/3 x 100 = 66 2/3 % Q.3 : 72 % of 25 students are good in Mathematics . How many are not good in Mathematics ? Sol : No. of st. good in maths = 75 % No. of st. not good in maths = (100 – 72) = 28 % of 25 = 28/100 x 25 = 7 st. Q.4 : A football team won 10 matches out of the total no. of matches they played . If their win % was 40 , then how many matches did they play in all ? Sol : Let they played games in all be x . The no. of games won by f.b. t.= 40% of x = 40/100 x (x) = 2x According to the Q. : 2x/5 = 10 x = 10 x 5/2 = 25 Therefore, 7 st. are not good in Mathematics. Q.5 : If Chameli had Rs 600 left after spending 75% of her money, how much did she have in the beginning ? Sol : let the t.money she had in the beginning was Rs x. The money she had spent = 75% of Rs x = 75/100 x (x) = Rs 3x/4 Money she had left = Rs x – Rs 3x/4 = Rs {x – 3x/4} = Rs x/4 According to the question ; x / 4 = 600 x = 600 x 4 = Rs 2400 Therefore , the money she had in the beginning was Rs 2400 . q.6 : If 60% people in a city like cricket, 30% like football and the remainig like other games then what % of the people like other games ? If the total no. of people are 50 lakh, find the exact no. who like each type of game ? Sol :% of p. like o.game = [100 – (60+ 30)% = (100 – 90) % = 10 % Total no. of people = 50 lakh = 50,00,000 No. of people like cricket = 60 % of 50,00,000 = 60/100 x 50,00,000 = 3,00,000= 3 lakh No. of people like football = 30% of 50,00,000 = 30/100 x 50,00,000 = 15,00,000 = 15 lakh No. of like people o. games = 10% of 5000000 = 10/100 x 5000000 = 5,00,000 = 5 lakh Therefore, 3 lakh people like cricket, 15 lakh people like football & 5 lakh people like other games . Exercise : 8.2 Q.1 : A man got a 10% increase in his salary . If tis new salary is Rs 1,54,000, find his original salary ? Sol : Let his original salary be Rs (x) . Increase in his salary = 10% of Rs (x) =10/100 x (x) = Rs x/10 New salary = o. salary + i. salary = Rs x + Rs x/10 = Rs 11x/10 According to the question ; 11x/10 = 154000 (x) = 154000 x 10/11 (x) = 1,40,000 Therefore, his original salary is Rs 1,40,000. Q.2 : On Suday 845 people went to the Zoo. On Monday 169 people went . What is the % decrease in the visiting the Zoo on Monday? Sol : No. of people went to Zoo on Sunday = 845 people No. of people went to Zoo on Monday = 169 people Decrease in no. of people visiting the Zoo = 845 – 169 ( people ) = 676 people % decrease in the no. of people visiting the Zoo = 676/845 x 100% = 80% Therefore, the % decrea % .se in the people visiting the Zoo on Monday is Q.3 : A shopkeeper buys 80 articles for Rs 2,400 and sells them for a profit of 16 %. Find the selling price of one article ? Sol : C.P. of 80 articles = Rs 2,400 Profit = 16 % of Rs 2,400 = 16/100 x 2,400 = Rs 384 S.P. of 80 articles = C.P. + Profit = Rs 2,400 + Rs 384 = Rs 2,784 S.P. of 1 article = Rs 2,784/80 = Rs 34.80 Therefore, the selling price of one article is Rs 34.80 q.4 : The cost of an article was Rs 15,500, Rs 450 were spent on its repairs . If it is sold for a profit of 15%, find the selling price of the article ? Sol : C.P. of an article = Rs 15,500 + Rs 450 = Rs 15,950 Profit = 15% of Rs 15,950 = 15/100 x 15,950 =Rs 2,392.50 S.P. of an article = C.P. + Profit = Rs 15,950 + Rs2,392.50 = Rs 18,342.50 Therefore, the selling price of the article is Rs 18,342.50 q.5 : A VCR and TV were bought for Rs 8,000 each. The shopkeeper made a loss of 4% on the VCR and a 8% on the TV. Find thegain or loss % on the whole transaction ? Sol : Combined C.P. of the both VCR and TV = Rs 8,000 + Rs 8,000 = Rs 16,000 Loss of 4% on the VCR = 4/100 x 8,000 = Rs 320 S.P. of the VCR = C.P. – Profit = 8,000 – 320 = Rs 7,680 Profit of 8% on the TV = 8/100 x 8,000 = Rs 640 S.P. of the TV = C.P. + Profit = 8,000 + 640 = Rs 8,640 Combined S.P. = Rs 7,680 + Rs 640 = Rs 16,320 Gain of the whole transaction = S.P. – C.P. = Rs 16,320 – Rs 16,000 = Rs 320 Gain % = 320/16,000 x100 = 2% Therefore, the gain % on the whole transaction is 2% . q.6 : During a sale, a shop offered a discount of 10% on th M.P. of all the items. What would a customer have to pay for a pair jeans marked at Rs 1,450 and two shirts marked at Rs 850 each ? Sol : M.P. of a pair of Jeans = Rs 1,450 M.P. of a Shirt = Rs 850 M.P. of the two Shirts = Rs (2 x 850) = Rs 1,700 T.M.P. of a pair of Jeans and Shirts = Rs 1,450 + Rs 1,700 = Rs 3,150 Discount of 10% = 10/100 x 3,150 = Rs 315 S.P. = T.M.P. – Discount = Rs 3150 – Rs 315 = Rs 2835 Therefore, the customer will have to pay Rs 20,000 each for a pair of jeans and two shirts . q.7 : A milkman sold two of his buffaloes for Rs 20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss ? Sol : C.P. of both the two buffaloes be (x) and (y) . S.P. of each buffalo = Rs 20,000 C.P. of the first buffalo = S.P. x 100/100 + 5 = 20,000 x 100/105 = 4,00,000/21 C.P. of the second buffalo = S.P. x 100/100 – 10 = 20,000 x 100/90 = 2,00,000/9 Over-all loss = C.P. – S.P. = 4,00,000/21 + 2,00,000/9 – 40,000/1 = 12,00,000 + 14,00,000 – 25,20,000/63 = 80,000/63 = Rs 1,269.84 q.8 : The price of a TV is Rs 13,000. The sales tax charged on it is at the rate of 12%. Find the amount that Vinod will have to pay if he buys it ? Sol : C.P. of the T.V = Rs 13,000 Sales tax charged on it = 12% of 13,000 = 12/100 x 13,000 = Rs 1,560 S.P. = C.P. + Sales tax = Rs (13,000 + 1,560) = Rs 14,560 q.9 : Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is Rs 1,600, find the marked price ? Sol : Let the M.P. be Rs (x) . Discount of 20% = 20/100 x (x) = Rs x/5 S.P. = M.P. – Discount = Rs x – Rs x/5 = Rs 4x/5 According to the question ; 4x/5 = 1,600 x = 1,600 x 5/4 x = Rs 2,000 Therefore, the M.P. of the pair of skates is Rs 2,000 . q.10 : I purchased a hair – dryer for Rs 5,400 including 8% VAT. Find the price before VAT was added ? Sol : When the price including VAT is Rs 108 , Original price = Rs 100 When price including VAT is Rs 5,400 , Original price = Rs 100/108 x 5,400 = Rs 5,000 Therefore, the price before VAT was added is Rs 5,000 Exercise : 8.3 q.1 : Calculate the amount and compound interest on : (a): Rs 10,800 for 3 years at 12 ½ % per annum compounded anually . Sol : P : Rs 10,800 R : 12 ½ % = 25/2 % T : 3 years A = P ( 1+R /200 ) n 1 3 = 10,000 1 + 25 2008 ( ) ( ) () = 10,000 8 + 1 8 = 10,000 9 8 672 1350 3 3 = 10,000 x 9 x 9 x 9 8 8 8 4 1 = 675 x 9 x 9 x 9 8 = 675 x 729 32 = 4,92,075 32 = Rs 15,377.34 C.P. = A – P = 15,377.34 – 10,800 = Rs 4,577.34 (b) : Rs 18,000 for 2 ½ year ay 10% per annum compounded annualy . Sol : P ; Rs 18,000 R : 10% T : 2 ½ year A = P ( 1+R /100 ) n 2 = 18,000 1+10 100 ( ) ( ) = 18,000 10 + 1 10 2 2 () = 18,000 11 10 = 18,000 x 11 x 11 10 10 = 180 x 121 = Rs 21,780 S.I. = PRT = 21,780 x 10 x ½ 100 = Rs 1,089 C.I. = A – P = 21,780 – 18,000 = Rs 3,80 T.C.I. = 3,780 + 1,089 = Rs 4,869 A of 2 ½ year = P + I = 21,780 + 1,089 = Rs 22,869 (c) : Rs 62,500 for 1 ½ year at 8% per annum compounded half yearly . Sol : P = Rs 62,500 R = 8% = 4 years T = 1 ½ year =3 n A=P 1+R 100 ( ) ( ) = 62,500 1 + 4 100 3 ( ) () = 62,000 25 + 1 25 = 62,500 4 100 2,500 3 26 25 3 = 62,500 x 26 x 26 x 26 25 25 25 1 1 = 4 x 26 x 26 x 26 = Rs 70,304 1 C.I. = A – P = 70,304 – 62,500 Rs 7,804 (d) : Rs 8,000 for 1 year at 9% per annum compounded half yearly . Sol : P = Rs 8,000 R = 9% = 9/2 T = 1 year n A=P 1+R 200 ( ) ( ) = 8,000 1 + 9 200 2 ( ) ( ) = 8,000 200 + 9 200 = 8,000 42 2 2 209 200 = 8,000 x 209 x 209 200 200 10 1 = 2 x 209 x 209 10 = 47,362 10 = Rs 8,736.2 C.I. = A – P = 8,736.2 – 8,000 = Rs 736.2 (e) : Rs 10,000 for 1 year T 8% per annum compounded half yearly . Sol : P = Rs 10,000 R = 8% = 4% T = 1 year =2 n A=P 1+R 100 ( ) ( ) 1 = 10,000 1 + 4 25100 2 ( ) ( ) = 10,000 25 + 1 25 = 10,000 16 100 26 2 25 = 10,000 x 26 x 26 25 25 = 16 x 26 x 26 = Rs 10,816 2 C.I = A – p = 10,816 – 10,000 = Rs 816 q.2 : Kamala borrowed Rs 26,400 from a bank to buy a scooter at a rate of 15% p.a. compounded annually . What amount will she pay at the end of 2 years and 4 months to clear the loan ? Sol : P = Rs 26,400 R = 15% T = 2 years, 4 months = 2 y. and 1/3 y. =2 2 ( ) ( ) ( ) () A = P 1+ R 100 3 = 26,400 1+15 100 20 = 26,400 20+3 20 = 26,400 23 20 132 2 2 2 66 = 26,400 x 23 x 23 20 20 = 66 x 23 x 23 = Rs 34,914 S.I. = PRT = 34,914 x 15 x 1 100 100 x 3 = 34,914 x 5 100 = 1,74,570 100 = Rs 1,745.70 1 T.A = 34,914 + 1,745.70 = Rs 36,659.70 C.I = A – P = 36,659.70 – 26,400 = Rs 10,259.70 q.3 : Fabina borrows Rs 12,500 at 12% per annum for 3 years at S.I and Radha borrows the same amount for the same time period at 10% per annum , compounded annually . Who pays more interest and by how much ? Sol : For Fabina ; P = Rs 12,500 R = 12% T = 3 years S.I = PRT = 12,500 x 12 x 3 100 100 = 125 x 12 x 3 = Rs 4,500 For Radha ; P = Rs 12,500 R = 10% T = 3 years A=P n ( ) ( ) ( ) () 1+R 100 = 12,500 1 + 10 100 = 12,500 10 + 1 10 = 12,500 11 10 3 3 =12,500 x 11 x 11 x 11 10 10 10 = 125 x 11 x 11 x 11 10 = 1,66,375 10 = Rs 1,66,375.50 C.I = A – P = 1,66,375.50 – 12,500.00 = Rs 4,137.50 Difference between C.I and S.I ; = 4,500.00 – 4,137.50 = Rs 362.50 Therefore , Fabina pays more money by Rs 362.50 than Radha . q.4 : I borrowed Rs 12,000 from jamshed at 6% per annum simple interest for 2 years . Had I borrowed this sum at 6% per annum coumpound , what exess amount would I have to pay ? Sol : P = Rs 12,000 R = 6% T = 2 years S.I = PRT = 12,000 x 6 x 2 100 100 = 120 x 12 = Rs 1,440 A=P n ( ) ( ) ( ) () 1+R 100 3 2 = 12,500 1 + 6 100 50 = 12,500 50 + 3 50 = 12,500 24 53 50 2 = 12,500 x 53 x 53 50 1 50 2 = 24 x 53 x 53 = Rs 13,483.20 C.I = A – P = 13,483.20 – 12,000.00 = Rs 1,483.20 Excess A = 1,483.20 – 1,440.00 = Rs 43.20 Therefore , I would have to pay to him an excess amoun of Rs 43.20 . q.5 : Vasudevan invested Rs 60,000 at an interest rate of 12% per annum compouunded half yearly . What amount would he get (i) After 6 months ? Sol : P = Rs 60,000 R = 12% = 6% T = ½ year = 1 half year ( A=P 1+R 100 n 1 ( ) ( ) () = 60,000 1 + 6 100 1 = 60,000 100 + 6 100 = 60,000 106 1 100 = 60,000 x 106 100 = 600 x 106 = Rs 63,600 There fore , he would get Rs 63,600 after 6 months . (ii) : After 1 year ? Sol : P = Rs 60,000 R = 12% = 6% T = 1 year =2 n A=P 1+R 100 ( ) ( ) 3 = 60,000 1 + 6 100 50 2 ( ) () = 60,000 50 + 3 = 60,000 120 2 53 2 =60,000 x 53 x 53 50 50 1 24 = 120 x 53 x 53 5 1 = 24 x 53 x 53 = Rs 67,416 q.6 : Arif took a loan of Rs 80,000 frm a bank . If the rate of interest is 10% per annum , find the difference in amounts he would be paying after 1 ½ years if the interest is ; (i) : Compounded annually ? Sol : P = Rs 80,000 R = 10% T = 1 ½ year = 1 year ( ( ( ( ( ( 1+R 100 ( A=P n = 80,000 1 + 10 100 = 80,000 10 + 1 10 = 80,000 x 11 10 ( = 80,000 11 10 1 1 1 = 8,000 x 11 = Rs 88,000 4,400 S.I = PRT = 88,000 x 10 x 1 100 2 x 100 1 = Rs 4,400 (ii) : Compounded half – yearly ? Sol : P = Rs 80,000 R = 10% = 5% T = 1 ½ years =3 n A=P 1+R ( ) ( ) 100 1 = 80,000 1 + 5 100 20 3 ( ( ( = 80,000 20 + 1 20 40 3 ( = 80,000 21 20 10 20 3 = 80,000 x 21 x 21 x 21 1 20 1 20 1 20 = 10 x 21 x 21 x 21 = Rs 92,610 q.7 : Maria invested Rs 8,000 in a business. She would be paid interest at rate of 5% per annum compounded annually . Find ; (i) : The amount credit against her name at the end of the second year . Sol : P = Rs 8,00 R = 5% T = 2 years n A=P 1+R 100 ( ( ( ( = 8,000 1 +15 2 100 ( ( ( 20 = 8,000 20 + 1 20 2 ( = 8,000 21 20 20 400 2 = 8,000 x 21 x 21 1 20 1 20 = 20 x 21 x 21 = Rs 8,820 (ii) : The interest for the third year . Sol : P = Rs 8,820 R = 5% T = 1 years n A=P 1+R 100 ( ( = 8,820 1 + 5 100 20 1 ( ( ( ( 1 = 8,820 20 + 1 20 1 ( ( = 8,820 21 20 441 1 = 8,820 x 21 1 20 = 441 x 21 = Rs 9,261 q.8 : Find the amount and the compound interest on Rs 10,000 for 1 ½ years at 10% per annum, compounded half yearly . Would this interest be more than the interest he would get if it was compounded annually ? Sol : P = Rs 10,000 R = 10% = 5% T = 1 ½ years =3 Compounded haif - yearly n A=P 1+R 100 ( ) ( ) ( ) () = 10,000 1 1+5 100 20 = 10,000 20 + 1 20 = 10,000 21 20 3 3 3 = 10,000 x 21 x 21 x 21 20 20 20 = Rs 11,576.25 C.I = A – P = 11,576.25 – 10,000 = Rs 1,576.25 There fore , the interest when compounded half yearly would be more than the interest when compounded annually . q.9 : Find the amount which Ram will get on Rs 4,096 , if he gave it for 18 months at 12 ½ years per annum , interest being compounded half - yearly ? Sol : P = Rs 4,096 R = 12 ½ % = 25/2% =1/2 x 25/2% = 25/4% T = 18 months =3 n A=P 1+R 100 ( ) = 4,096 1 + 25 3 4 x 100 ( ) ( ) ( ) ( ) 1 = 4,096 1 + 25 3 400 16 = 4,096 16 + 1 3 16 = 4,096 17 3 16 = 4,096 x 17 x 17 x 17 16 16 16 = Rs 4,913 There fore , the required amount is Rs 4,913 . Muliple choise question q.1 : The fraction 2/5 converted to % age is: (a) : 20% (c) : 40% (b) : 30% (d) : 50% Q.2 : The marked price of a book is Rs 100 . The shopkeeper give 25% discount on it . What is the sale price of the book ? (a) : Rs 100 (c) : Rs 25 (b0 : Rs 125 (d) : Rs 75 Q.3 : A toy marked at Rs 40 is available for Rs 32 . What % discount is given on the marked price ? (a) : 10% (c) : 25% (b) : 20% (d) : 40% Q.4 : Meenu purchased a fridge for Rs 10,000 and sold it for Rs 8,000 . Find her loss . (a) Rs 8,000 (c) : Rs 2,000 (b) : Rs 10,000 (d) : Rs 12,000 Q.5 : Saroj purchased a watch for Rs 1,000 and she sold it for Rs 1,200 . What is her profit ? (a) : Rs 1,000 (c) : Rs 200 (b) : Rs 1,200 (d) : Rs 800 Q.6 : Kanti purchased a sewing machine for Rs 2,000 . She sold it at a loss of 40% . Find the selling price . (a) : Rs 1,200 (c) : Rs 800 ( b) : Rs 400 (d) : Rs 2,800 Q.7 : Rani purchased a T.V for Rs 10,000 and sold it for Rs 8,000 . Find her loss % . (a) : 10% (c) : 40% (b) : 20% (d) : 60% Q.8 : Sapna purchased a cycle for Rs 1,000 and sold it for Rs 1,200 . Find her gain %. (a) : 20% (c) : 40% (b) : 10% (d) : 12% Q.9 : Find the simple interest on Rs 1,000 for 2 years at 8% per annum . (a) : Rs 80 (c) : Rs 120 (b) : Rs 40 (d) : Rs 160 Q.10 : A sofa set was brought for rs 10,000. Its value depreciated at the rate of 10% per annum. Find its value after one year . (a) : Rs 11,000 (c) : Rs 10,000 (b) : Rs 9,000 (d) : Rs 1,000 Q.11 : There are 1,275 trees in Chaudary Farm. Out of these 36% trees are of fruits. How many trees of fruits are there in Chaudary Farm ? (a) : 459 (c) : 549 (b) : 945 (d) : 954 Q.12 : The salary of Manish is Rs 10,000. His salary gets increased by 10% . Find his increased salary . (a) : Rs 9,000 (c) : Rs 8,000 (b) : Rs 11,000 (d) : Rs 12,000 Q.13 : The simple interest 0n Rs 2,000 for 4 years is Rs 400 . The rate % of interest is : (a) : 2,000 x 100/400 x 4 (b) : 400 x 4/2,000 x 100 (c) : 400 x 100/2,000 x 4 (d) : 2,000 x 4/400 x 100 Q.14 : a sum is taken for one year at 9% p.a. If interest is compounded after every three months, how many times will interest charged in one year ? (a) : 2 times (c) : 4 times (b) : 3 times (d) : 1 time Answers are in the next slide : Solutions : (1) : 40 % (2) : Rs 75 (3) : 20% (4) : Rs 2,000 (5) : Rs 200 (6) : Rs 1,200 (7) : 20% (8) : 20% (9) : Rs 160 (10) : Rs 9,000 (11) : 459 (12) : Rs 11,000 (13) : 400 x 100/2,000 x 4 (14) : 4 times