Saleem has 40 articles of same cost price. He sold 24 articles at a profit of 30% and 16 articles at a profit of 20%. Had he sold all the articles at a profit of 15%, then his profit would have been reduced by Rs. 880. What is the cost price (in Rs.) of each article?
सलीम के पास समान क्रय मूल्य की 40 वस्तुएँ हैं। उसने 24 वस्तुओं को 30% के लाभ पर और 16 वस्तुओं को 20% के लाभ पर बेचा। यदि वह सभी वस्तुओं को 15% के लाभ पर बेच देता, तो उसका लाभ 880 रुपये कम हो जाता। प्रत्येक वस्तु का लागत मूल्य (रु में) क्या है?
Sohan bought an old Honda Bike and spent Rs. 1500 on its repairs. Then Sohan sold it to Rakesh at a prolit of 20%. Rakesh sold it to Raj at a loss of 10%. Raj finally sold it for Rs. 12100 at a profit of 10%. How much did Sohan pay for the old Honda Bike?
सोहन ने एक पुरानी होंडा बाइक खरीदी और उसकी मरम्मत पर 1500 रुपये खर्च किए। सोहन ने इसे राकेश को 20% के लाभ पर बेच दिया। राकेश ने इसे 10% की हानि पर राज को बेच दिया। अंत में राज ने इसे 10% के लाभ पर 12100 रुपये में बेच दिया। सोहन ने पुरानी होंडा बाइक के लिए कितना भुगतान किया?
Sourav Ganguly wants to buy a total of 100 sports equipment using exactly a sum of Rs.1000. He can buy ball at Rs.20 per unit, wicket at Rs.5 per unit and bat at Rs.1 per unit. If he has to buy at least one of each equipment and cannot buy any other type of equipment, then in how many distinct ways can he make his purchase?
Let the number of ball, wickets and bats purchased be A, B and C, respectively.
Thus,
20A + 5B + C = 1000 and A + B + C = 100
Solving the above two equations by eliminating C, we Get
19A + 4B = 900
⇒ B = 225 –
19
A
4
Now, as B is the number of wickets and 0 < B < 99,
So, putting these limiting values of B in the above equation will provide the value of A as 27 < A < 47.
Since A has to be the multiple of 4, so possible values of A are 28, 32, 36, 40 and 44.
Now, for A = 28 and 32; A + B > 100, so these values of A can be rejected.
For all other values of A, we get the desired solution:
A = 36, B = 54, C = 10
A = 40, B = 35, C = 25
A = 44, B = 16, C = 40
Thus, there are three possible solutions.
Hence, option (C) is correct.
3
सौरव गांगुली 1000 रुपये की राशि का उपयोग करके कुल 100 खेल उपकरण खरीदना चाहते हैं। वह गेंद को 20 रुपये प्रति यूनिट, विकेट 5 रुपये प्रति यूनिट और बल्लेबाजी 1 रुपये प्रति यूनिट की दर से खरीद सकते हैं। यदि उसे प्रत्येक उपकरण में से कम से कम एक उपकरण खरीदना है और वह किसी अन्य प्रकार के उपकरण को नहीं खरीद सकता है, तो वह कितने अलग-अलग तरीकों से खरीद सकता है?
Let the number of ball, wickets and bats purchased be A, B and C, respectively.
Thus,
20A + 5B + C = 1000 and A + B + C = 100
Solving the above two equations by eliminating C, we Get
19A + 4B = 900
⇒ B = 225 –
19
A
4
Now, as B is the number of wickets and 0 < B < 99,
So, putting these limiting values of B in the above equation will provide the value of A as 27 < A < 47.
Since A has to be the multiple of 4, so possible values of A are 28, 32, 36, 40 and 44.
Now, for A = 28 and 32; A + B > 100, so these values of A can be rejected.
For all other values of A, we get the desired solution:
A = 36, B = 54, C = 10
A = 40, B = 35, C = 25
A = 44, B = 16, C = 40
Thus, there are three possible solutions.
Hence, option (C) is correct.
C
4
In St. Peter’s college Agra an exhibition was organised, hand-made crafts are displayed for sale. Some students are assigned the work of selling crafts. The overall profit p depends on the number of students x selling the crafts on that particular day and is given by the equation p = 250x – 5x2. The school manager claims to have made a maximum profit. Find the number of students engaged in selling the crafts and the maximum profit made.
For profit to be maximum, the derivative of p with reference to x must be 0 and hence
=
d (250x – 5x2)
= 0 = 250 – 10x = 0
dx
So x = 25
Now p for x = 25 is
= 250 (25) – 5 (25)2 = Rs3125
Hence, option (C) is correct.
4
सेंट पीटर्स कॉलेज आगरा में एक प्रदर्शनी का आयोजन किया गया था, हाथ से बने शिल्प बिक्री के लिए प्रदर्शित किए जाते हैं। कुछ छात्रों को शिल्प बेचने का काम सौंपा गया। कुल लाभ p उस विशेष दिन पर शिल्प बेचने वाले x छात्रों की संख्या पर निर्भर करता है और समीकरण p = 250x – 5x2 द्वारा दिया जाता है। स्कूल मैनेजर का दावा है कि उसने सबसे ज्यादा मुनाफा कमाया है। शिल्प को बेचने में लगे छात्रों की संख्या और अधिकतम लाभ ज्ञात कीजिए।
For profit to be maximum, the derivative of p with reference to x must be 0 and hence
=
d (250x – 5x2)
= 0 = 250 – 10x = 0
dx
So x = 25
Now p for x = 25 is
= 250 (25) – 5 (25)2 = Rs3125
Hence, option (C) is correct.
C
5
The marked price of an article is Rs. 3,000. If two successive discounts, each of x%, on the marked price is equal to a single discount of Rs. 1,174.80, then what will be the selling price of the article if a single discount of x% is given on the marked price?
एक वस्तु का अंकित मूल्य 3,000 रुपये है। यदि अंकित मूल्य पर दो क्रमागत छूट, प्रत्येक x%, 1,174.80 रुपये की एकल छूट के बराबर है,तो वस्तु का विक्रय मूल्य क्या होगा यदि अंकित मूल्य पर x% की एकल छूट दी जाती है?
