ANSWERS AND EXPLANATIONS EXERCISE 1
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1 1 ANSWERS AND EXPLANATIONS EXERCISE 1 1. (a) Percentage profit 0% 1. (c) CP ` 60 SP 4 of ` (a) Let the cost price of the article be ` x. Then, (84 x) 6 x l68 x 6 x x `7 4. (e) If no discount is given, selling price of TV 1740 `1500 Cost price of TV 1740 ` Gain % 0% (a) List price of calculator 8.50 ` 75 0 Deepa bought calculator in ` (e) Let the marked price (SP) ` x According to the question, 75% of x or, x ` (e) CP of DVD player ` x According to the question, x 1 ` 80 x ` (a) Let the cost price be ` x Now, according to the question, 18 x x ` 550. (d) CP of kg of sugar ` 7 CP of 1 kg of sugar ` 7 CP of 15 kg of sugar 7 ` 15 `474. (a) Required price ( ) (8 + 8) ` 16. (e) Let the cost price of a toy be `x According to the question, x or x ` ` (a) CP of television set 500 ` 15 `00 1. (e) Cost of 1 kg of sugar `15 Cost of 1 kg of sugar ` 15 1 Cost of 1 kg sugar 15 1 `15 1 Similarly, 6 kg of rice `8 17 Cost of 1 kg of wheat 6 1 `04 1 Total cost ( )` ` (e) Let the original selling price of watch `x According to the question,
2 14 PRPFIT AND LOSS x or, x `5 15. (e) Cost of 6 gms of gold Cost of 4gms of silver Cost of 5 gms of silver `64 6 ` `7800 Total cost ( ) ` (b) Required cost price (b) Cost price ` 450 ` (c) 4 bats + sticks ` ( bats + 4 sticks) ` 5600 bats + 4 sticks ` (a) The cost of 4 cell-phones and 7 digital cameras `1567 cost of 8 cell-phones and 14 digital cameras ( 1567) ` (b) Let the CP of a calculator and pen-stand be ` x and ` y respectively. According to the question, x + 4y 140 x + 5y (i)...(ii) x + 4y 140 (i) 5 equation (ii) 4 15x + 0y 4x 0y x 580 x 580 `480 4 CP of 4 calculators ` (4 480) ` (a) Cost price ` 16. (c) Required amount 500 ` (e) 15 pendants + 4 chains (5 pendants + 8 chains) ` (a) Original selling price ` (d) Selling price 5600 ` Loss percent ( ) % 6. (b) Required cost ` (b) Let S.P. `. Then, C.P. ` 6; Profit ` 4. Profit % 4 5 % % 4.17%. 6 4.% 6 8. (a) Let the cost of production of the table be ` x. Then, 15% of 5% of 1% of x x x 165 x Rs
3 . (d) C. P. for 50 pencils ` C. P. for 45 pencils S.P. of 45 pencils No gain, no loss 0. (c) Retailer s S.P. M.P. 45 Rs.0 50 Retailer s C.P. for 0 Pens M.P. of 7 pens Retailer s S.P. for 0 pens M.P of 0 pens % gain % 7 1. (a) Let M.P. ` then discount ` 16 when discount ` 80, then M.P ` x Now, x : x : : 16 : 80 16x 80 x ` 500 it s direct proportion Now, since M. P. ` 500, therefore, after 16% discount man paid Rs 40. (c) Let C.P. `. Then M.P. ` and S.P. ` 8 % discount. (b) Offering price 1 % % 508 Rs54 After % discount, S.P. 0% of (c) Let A paid ` x 054 Rs % of % of x 5 15 x 5 5 x Rs (c) C.P. for B % of ` 400 ` 480 Rs C.P. for C 1% of ` 480 ` (c) C.P ` 00 Remaining eggs Let S.P. of eggs ` x per dozen Total S.P. ` 560 x ( 5)% x x Rs. 4.5per dozen (d) Let C. P. ` x. Then 8. (b) C.P. S.P 1 S.P ` 6 ( )x ( 8)x 6 1 Rs x 8 x 600 x 600 x ` Rs 15 7 ` % gain 5% EXERCISE 1. (a) Purchase price ` 480 Repair cost 0% of ` 480 ` 6 Total cost ` ` 6 ` 576 Net profit ` 144 Selling price Total cost + Net profit ` ` 70 Now, Selling price - Purchase price ` 70 ` 480 ` 40 Reqd percentage ` 40 ` %
4 16 PRPFIT AND LOSS. (a) Let the price of one saree and one shirt be ` x and ` y respectively. Then, x + 4y 1600 or, x + y (i) Also, x + 6y (ii) Solving equations (i) and (ii), we get 4y 800 or, y 00 cost of 1 shirts 1 00 ` 400. (b) CP of 150 calculators ` 7,500. total CP 7, ` 40,000 Marked price of 150 calculators ` 48,000 Selling price after discount ` 45,600 Percentage profit 45,60040,000 14% 40, (b) C.P. of 00 kg of mixture `( ) ` 000. S.P. 6% of `000 6 ` 000 ` 480. Rate of S.P. of the mixture 480 ` per kg 00 ` per kg. 5. (b) Let profit per litre ` 0 So, C.P. / litre ` S.P. / litre ` On adding % water to the milk C.P./ litre ` S.P./ litre ` S.P. / litre 400 ` ` Profit / litre 400. % by which profit increases (a) S.P. of the 1st chair ` 500 Gain 0% C.P. of the 1st chair 150 S.P. of the nd chair ` 500 Loss 1% C.P. of the nd chair Now S.P. of both the chairs ` 0 C.P. of both the chairs Net gain Gain % % (To one place of decimal) (a) Women's shirt comprise 60% of the output. Men's shirts comprise ( 60) 40% of the out put. Average profit from men's shirt 8% of 40. out of 40 Overall average profit 6 out of Average profit from women's shirts.8 out of 60 i.e out of each shirt. d1 d 8. (c) Retailer price list price 1 1
5 17 d d d (1 0.85) 15%. (b) ( loss) : S 1 : : ( + gain) : S ( 1.5) : 40 : : ( + 1.5) : S 87.5 : 40 : :.5 : S 87.5 S S (c) Let the value of radio be ` x. Then C. P. % profit Rs x, S. P. 4 6 x x % x 4. (b) ( 0) : 45 : : ( + 0) S 45 S Rs (d) C.P. for 1 lichchu paise S. P. for 1 lichchu paise 0 6 x 1 x 5 1 : ( 4) :: x : ( 8) x 66 He sells oranges per rupee. 15. (b) C.P. for one coconut S.P. for one coconut ` Profit on one coconut Profit on 000 coconut 150 Rs Rs 1 Rs 16. (a) Let C.P. `, then M. P. ` 150 S.P. 70% of 150 ` 5 % profit 17. (a) C.P. for one orange Then S.P. 5 5% 1 Rs Rs 0 ( 5) Hence S.P. for one orange 1 Rs 1 1 oranges must be sold for a rupee to gain 5%. 18. (b) C.P. of one litre ` 6 After adding water to it gain % 1% One has to pay ` 7.0 for litre of milk. So S.P. of litre of milk ` (b) S.P. for 1 egg ` 5 1 Rs 1 5 C. P. for 1 egg Rs ( 0) 1 He bought 1 eggs for 5 rupees. 14. (c) Let he sells x oranges per rupee. 7.0 S.P. of 1 litre of milk Rs Rs.80 S.P. C.P Hence gain %
6 18 PRPFIT AND LOSS 1. (b) Let profit per litre ` 0 So, C.P. / litre ` S.P. / litre ` On adding % water to the milk 4. (b) Let the C.P. of horse ` x Then the C.P. of carriage ` (000 x) 0% of x % of (000 x) % of 000 C.P. per litre Rs S.P. per litre Rs S.P. per litre Profit / litre 400 Rs Rs 400. % by which profit increases (d) Let C.P. ` x. Then, S.P. ( 7) x x Also, x 48 x ( 5) x x 1x 4800 x ` (a) C.P. of 150 calculators. (b) ` Labelled price of 150 calculators ` Discount allowed 5% S.P. of 150 calculators % of ` Profit % True weight gain% False weight x Here S.P. C. P. x 0 0 False weight 800 gm 15. (c) Let cost Price ` Marked price ` 15 After discount, selling price Profit%.5 1.5% x (000 x) 60 5 x 000 x 600 x 600 x 0 5. (d) Here, SP 1 SP 140 CP 1 60CP CP1 6 CP 14 7 CP Rs 400 ( 7) and CP ` (a) Let S.P. ` x per kg S.P. of 4 kg ` 4x 4x x Rs (a) Let C.P. of one orange Re 1 Then C.P. of 8 oranges ` 8 S.P of 8 oranges ` Gain % % (c) Let C.P. of 1 article Re 1 then C.P. of 5 articles ` 5 and S.P. of 5 articles ` 0 loss % 5 0 5% 0. (d) Let C.P. of one metre of cloth ` 1 then C.P. of 66 metres of cloth ` 66 Gain C.P. of metres ` 1 % gain % 66
7 Shortcut method : If on selling x articles, a man gains equal to the C.P. of y articles, then % gain 1 % gain % 66 y x 0. (b) Loss C.P. of 66 metres S.P. of 66 metres S.P. of metres C.P. of 66 metres S.P. of 88 metres % loss loss C.P. of 66 metres S.P of metres C.P of 66 metres S.P. of metres S.P.of 88 metres 5% (b) Equivalent discount %. (b) Let the C.P. of the goods be ` Marked price of the goods ` Discount % S.P. is 0% of ` ` 8 Gain% (8 ) 8%. d. (d) For same article, 1 g1 d g g 0 g 015 g 150 g 75 50% 4. (c) SP 0 1. ` 8 Marked price 8 ` (d) Let the SP of the article be ` x Expenses 15% of x ` 0.15x 1 Profit % of x ` 0.x CP ` (given) Therefore, x + 0.1x x x 1 1 % increase for marked price 6. (c) ( + g 1 ) : S 1 : : ( + g ) : S % ( + 0) : 0 : : ( + g ) : 01 allowed on S.P.] : 0 : : ( + g ) : 7 7 g 8 0 g 8% 7. (b) Let C.P. `, Also, let M.P. ` x [ % discount is Given, C.P. after 0% discount on M.P. C.P. 80 % of x x Rs M.P. 5 % above C.P. 8. (c) Real profit % is the profit % on C.P. % profit on S.P. Real profit % % profit on S.P.. (c) Let the C.P. be ` S.P. ` 0 5% 0 Discount being 4%, S.P. is 6% of sale price. 6% of sale price ` sale price ` Rs.15 6 Sale price is 5% higher than the C.P. 40. (d) Let his loss ` x. Then, C.P x 5600 x x 600 x 00 C.P ` 500
8 0 PRPFIT AND LOSS EXERCISE 1. (d) Let x be no. of units. Profit per unit x (60 40) x 0x. Now, additional cost 000 To make a profit of at least ` 0 we have 0 x x 4000 x 00.. (d) Difference in rupees by increasing the price by rupees 1 is ` 50. That means that the quantity of milk is 50 litre. Now, equal containers will become 5 litre per container. x. (b) Profit, P 1 75 x C Constant PQ Price per quintal 0 C + 50Q...(1) and 80 C + 40Q...() on solving (1) and (), we get Q, C 500 Required expense (b) Let the original price of the jewel be ` P and let the profit earned by the third seller be x%. Then, ( + x)% of 15% of % of P 165% of P ( x) P P 165 ( x) 1 x % (b) Let C. P. ` x then profit S.P. C. P. For maximum P, dp 0 x 7.5 dx Taking x 7, and x 8, However x 7.5 Total P (a) Given total profit is 6% As given the out put of women shirt is 60% Mens output would be 40% Ratio of the profit of the women s shirt to men s shirt /5 : Contribution of men s /5 whereas women s Let Average profit in women s shirt be x. Given, Average profit in Men s shirt is 8% 6 8 x 5 5 x (c) We have Profit per sales of rupee is I C + PQ where I Monthly expense 1 x x 81 x x Rs8 8. (b) Let S. P. ` x per kg S.P. of kg of rice ` x Loss Now, Loss C.P. S.P. x 600 x x ` 50 per kg. (a) S.P. of the 1st chair ` 500 Gain 0% C.P. of the 1st chair 150 S.P. of the nd chair ` 500 Loss 1% C.P. of the nd chair
9 650 Now S.P. of both the chairs ` 0 C.P. of both the chairs Net gain Gain % % (To one place of decimal) (a) Women's shirt comprise 60% of the output. Men's shirts comprise ( 60) 40% of t h e out put. Average profit from men's shirt 8% of 40. out of 40 Overall average profit 6 out of Average profit from women's shirts.8 out of 60 i.e out of each shirt.. (c) Here, in whole transaction, there is neither gains nor loss, therefore, Amount of gain in one watch Amount of loss in other watch 0.15CP1 0.CP CP1 0. CP 0.15 Also CP 1 + CP 560 CP 560 Rs 4 ( ) 1 and CP ` 6 1. (b) Let the C.P. be ` First S.P. ` Second C.P. ` 0 Second S.P 15% of ` 0 `.50 Difference of two selling prices is ` 5 `.50 `.50 and C.P. of the article is ` But actual difference is ` 4. C.P. Rs. 4 Rs (a) Let the CP of the article be ` x. Then, SP ` 5x Now, new CP ` 5x and new SP 5x 1 According to the question 5x 5 5x 1 x ` 00 d1 d 14. (c) Retailer price list price 1 1 d d d (1 0.85) 15% 15. (a) Retailer s price % of 1% of ( % of 5) 1 5 Rs 6.6 Rs (c) Let C.P. ` x 5 % of % of x x 700 x (b) Let C.P. `. Then, marked price ` 150. S.P. 75% of ` 150 `.50 Gain % 1.50%
10 PRPFIT AND LOSS 18. (d) C.P. of 1 4 th. of goods 1 ` 840 ` 4 S.P. of these goods 80% of ` ` 168 Remaining cost of the goods ` 840 ` ` 60 Over all S.P. of the goods % of ` 840 ` 8 Remaining goods must be sold for ` 8 ` 168 ` 840 Gain % 1 % (c) Let the C.P. for the manufacturer be `. Then, C.P. for the wholesaler ` 8 C.P. for the retailer 8 + 0% of 8 ` C.P. for the customer ` 177 If the C.P. for the customer is ` 177, then the C.P. for the manufacturer is `. If the C.P. for the customer is ` 0.0, then the C.P. for manufacturer is 0. 0 ` (a) Let the CP of the sunglasses be `. Now, SP ` 15 New CP ` 75 New SP ` 5 Thus, if he sells for ` (15 5) 0 less, then CP If he sells for ` less, then CP Rs (c) Let the price of first grade cycles be ` x each and that of second grade cycles be ` y each. Now, 8x + y 150 Let he sells A grade cycle at a rate of ` z per bicycle. Then, 8z z or z + 66z or 8z or z 180 He should sell the first grade bicycles at a rate of ` (b) Let the CP of a pen and a book be ` x and ` y, respectively. 0.5x y (x + y) + 7 or 0.15y 0.05x 7... (1) and 1.05x + 1.1y (x + y) + 1 or 0.05x + 0.1y 1... () Solving (1) and (), We get, y ` 80. (d) CP of 500 cassettes `,50,000 SP of each set of 0 ( + 1) cassettes 75 Rs. 150 `.50 ` 6.50 SP of 500 cassettes including 500 free cassettes 6.50 `,6,50 Overall loss `,50,000 `,6,50 ` % loss
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