31.The marked price of a chair and a table are in the ratio 2 : 3 respectively. The shopkeeper gives a 20% discount on the chair. If the combined discount on both the chair and the table is 26%, then what will be the discount given on the table?

एक कुर्सी और एक मेज का अंकित मूल्य क्रमशः 2 : 3 के अनुपात में है। दुकानदार कुर्सी पर 20% की छूट देता है। यदि कुर्सी और मेज दोनों पर संयुक्त छूट 26% है, तो मेज पर दी गई छूट कितनी होगी?


Option”C” is correct

Let the discount percentage on table be x.

Ratio of the marked price of a chair and a table = 2 : 3

Marked price of the Chair = Rs 200x

Marked price of the Table = Rs 300x

⇒ Combined price = Rs (200x + 300x) = Rs 500x

Discount = 26%

⇒ Combined selling price = Rs 500x (1 – 26/100) = Rs 370

In 1st case,

⇒ Selling price of chair = Rs 200x (1 – 20/100) = Rs 160

In 2nd case,

⇒ Selling price of table = Rs 300x (1 – x/100) = Rs (300 – 3x)

According to Question,

⇒ Combined selling price = Selling price of chair + Selling price of table

⇒ 370 = 160 + (300 – 3x)

⇒ x = 30%

∴ The discount given on the table is 30%.

32.Rahul purchased 80 items from the market. 25% items of the total items were defective and the remaining items were sold at 50% profit. What will be the overall profit percentage?

राहुल ने बाजार से 80 वस्तुएं खरीदी। कुल वस्तुओं का 25% वस्तु खराब थी और शेष वस्तुओं को 50% लाभ पर बेचा गया था। कुल लाभ प्रतिशत क्या होगा?


Option”B” is correct

Let 80 items are bought for Rs. 80

So 1 item = Rs. 1

25% of 80 = 20

Remaining items = 80 -20 = 60

Cost of 60 articles = Rs. 60

According to question remaining items are sold at the profit of 50%

So selling price of 60 items = 150% of 60 = 90

Cost price of items = Rs. 80

Selling price of items = Rs. 90

Profit = 90 – 80 = 10

∴ Profit percentage = (10 / 80) × 100 = 12.5%

33. P, Q and R invest sum in the ratio of 7 : 4 : 9 respectively. If they earned total profit of Rs. 6680 at the end of year, then what is the total share of P and Q together?

P, Q और R क्रमशः 7 : 4 : 9 के अनुपात में धनराशि का निवेश करते हैं। यदि उन्होंने वर्ष के अंत में 6680 रुपये का कुल लाभ अर्जित किया, तो P और Q का एक साथ कुल हिस्सा क्या है?


Option”D” is correct

As they all invested for same time period

Share of P = (7/20) × 6680 = Rs. 2338

Share of Q = (4/20) × 6680 = Rs. 1336

∴ Sum of share of P and Q = 2338 + 1336 = Rs. 3674

34. The selling price of the first article is ₹ 470 and the cost price of the second article is ₹ 470. If there is a loss of 20% on the first article and a profit of 20% on the second article, then what will be the overall profit or loss percentage?

पहली वस्तु का विक्रय मूल्य ₹ 470 है और दूसरी वस्तु का क्रय मूल्य ₹ 470 हैं। यदि पहली वस्तु पर 20% की हानि और दूसरी वस्तु पर 20% का लाभ होता है, तो कुल लाभ या हानि प्रतिशत क्या होगा?


Option”A” is correct

There is loss of 20% on first article

S.P. of 1st = Rs. 470

C.P. of 1st = 470/.8 = 587.5

Similarly, S.P. of 2nd = 470 × 1.2 = 564

Total C.P. = 587.5 + 470 = 1057.5

Total S.P. = 470 + 564 =1034

Loss = 1057.5 – 1034 = 23.5

Loss% 23.5/1057.5 = 2.2%

35. The selling price of an article is 84% of its cost price. If the cost price is increased by 20% and the selling price is increased by 25%, what is the percentage increase/decrease in the loss with respect to the earlier loss?

एक वस्तु का विक्रय मूल्य इसके क्रय मूल्य का 84% है। यदि क्रय मूल्य में 20% की वृद्धि होती है और विक्रय मूल्य में 25% की वृद्धि होती है, तो पहले की हानि के संबंध में हानि में वृद्धि/कमी प्रतिशत क्या है?


Option”A” is correct

⇒ Let, the cost price of article = x

⇒ Selling price of article = 84x/100 = 21x/25

loss% = [(cost price – selling price)/100] × 100

⇒ Loss% = (x – 21x/25) × 100/x

⇒ 16%

⇒ New cost price = 120x/100 = 6x/5

⇒ New selling price = 21x × 125/25 × 100

⇒ New selling price = 21x/20

loss% = (cost price – selling price) × 100/cost price

⇒ Loss% = (6x/5 – 21x/20) × 100/6x/5

⇒ Loss% = 12.5 %

⇒ Decrease in losses = (16 – 12.5) × 100/16

⇒ 21.875%

Alternate Method

 Let CP = 100

SP = 84

Loss  16%

New CP = 120

New SP = 84 × 125/100 = 105

Loss% = (120 – 105)/120 × 100 = 12.5

Decrease in loss% = [(16 – 12.5)/16] × 100

Decrease in loss% = 21.875%

36. Case A. In a certain store, the profit is 340% of the cost. Case B. If the cost increases by 32% but the selling price remains constant, approximately what percentage of the selling price is the profit in case B?

केस A. एक स्टोर में, लाभ क्रय मूल्य का 340% है। केस B. यदि क्रय मूल्य 32% बढ़ जाती है, लेकिन विक्रय मूल्य स्थिर रहता है, विक्रय मूल्य का लगभग कितना प्रतिशत लाभ केस B में है?


Option”C” is correct

Let the cost price be Rs. 100 and the selling price be SP

⇒ Profit = (SP – CP) 

Profit = 340 % of CP = Rs. 340

⇒ 340 = SP – 100

⇒ SP = Rs. 440

After increase in cost price

New cost price = 100 + (32/100) × 100 ⇒ Rs. 132

New profit = 440 – 132 ⇒ Rs. 308

Profit on the selling price = (308/440) × 100

⇒ 770/11 = 70%

∴ The new profit is 70% of the selling price

37. A sells an item at 20% profit to B, B sells the same at 10% profit to C and receives Rs. 1,32,000.0. Had C purchased the same item from A, he would have spent 5% less than what he spent with B. What profit would A have made then?

A, B को 20% लाभ पर एक वस्तु बेचता है, B, C को 10% लाभ पर बेचता है और 1,32,000.0 रुपये प्राप्त करता है। यदि C ने A से वही वस्तु खरीदी होता, तो B के साथ खर्च की गयी राशि से  5% से कम खर्च होते, तो A ने क्या लाभ अर्जित किया होता?


Option”B” is correct

Cost price of the item for B = 1,32,000 × (100/110) = Rs. 1,20,000

Cost price of the items for A = 1,20,000 × (100/120) = Rs. 1,00,000

If C had purchased the items for A instead of B, then cost price for C = 1,32,000 × (95/100) = Rs. 1,25,400

∴ Profit of A = 1,25,400 – 1,00,000 = Rs. 25,400

38. Anil bought two articles A and B at a total cost of Rs. 10,000. He sold the article A at 15% profit and the article B at 10% loss. In the whole deal, he made no profit or no loss. Find the selling price of the article A.

अनिल ने 10,000 रु. की कुल मूल्य पर दो वस्तुएं A और B खरीदी। उसने वस्तु A को 15% के लाभ पर और वस्तु B को 10% की हानि पर बेची। पूरे सौदे में, उसे ना तो लाभ और ना ही हानि हुई। वस्तु A का विक्रय मूल्य ज्ञात कीजिए।


Option”D” is correct

Let the CP of two articles be A and B be x and y respectively.

According to Condition –

15% of x = 10% of y                    [∵ Profit on A = Loss on B]

⇒ x : y = 2 : 3

x = 2/5 × 10000       ∵ x + y = 10000

⇒ x = 4000

SP of article A = 4000 × (1 + 15%)

⇒ 4600

∴ The selling price of the article A is Rs. 4600

39. A dealer sells an article by allowing a 15% discount on its marked price and gains 12%. If the cost price of the article is increased by 10%, how much discount percentage should he allow now on the same marked price so as to earn the same percentage profit as before?

एक डीलर अंकित मूल्य पर 15% छूट देकर एक वस्तु बेचता है और 12% लाभ अर्जित करता है। यदि वस्तु के क्रय मूल्य में 10% की वृद्धि हुई है, पहले के समान लाभ अर्जित करने के लिए उसे अब उसी अंकित मूल्य पर कितने प्रतिशत छूट देना चाहिए?


Option”B” is correct

Let C.P of an article be 100 unit

⇒ For 12% profit S.P = 112 unit

15% discount on mark price

⇒ S.P = 85% = 112 unit

⇒ M.P = 100% = ?

⇒ M.P = (100 × 112)/85

⇒ M.P = 2240/17

If C.P increased by 10%

⇒ New S.P = 110 unit

⇒ For 12% profit new S.P = (110 × 112)/100

⇒ 616/5

Discount % = (M.P – S.P)/M.P × 100

⇒ (2240/17 – 616/5)/(2240/17) × 100

⇒ 6.5%

∴ The discount percentage should be allowed now on the same marked price is 6.5%

40. A shopkeeper earns a profit of 25% when he sells an article by allowing 20% discount on its marked price. If the cost price of the article is decreased by 20%, how much discount percent should he allow now on the same marked price so as to earn the same percentage of profit as earlier?

एक दुकानदार तब 25% लाभ अर्जित करता है जब वह अंकित मूल्य पर 20% की छूट देकर एक वस्तु को बेचता है। यदि वस्तु का क्रय मूल्य 20% तक कम हो जाता है, तो उसे उसी अंकित मूल्य पर कितना छूट प्रतिशत देना चाहिए ताकि पहले के समान लाभ का समान प्रतिशत अर्जित किया जा सके?


Option”B” is correct

Let the initial cost price be 100x 

Selling price = 100x + 25% of 100x 

⇒ 125x 

Selling price = Marked price – 20% of marked price 

Marked price = 625x/4 = 156.25x

Now Cost price got decreased by 20%, so new cost price 

New cost price = 80x 

New selling price = 80x + 25% of 80x 

⇒ 100x 

Discount per cent on marked price to get this selling price 

Discount per cent = (Marked price – selling price)/(Marked price) × 100 

⇒ (156.25x – 100x)/(156.25x) × 100 

⇒ 36% 

∴ Discount should be 36% 

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