1. Final Ratio between milk to water in a vessel is 64 : 61. If initially there was 100 L milk. Some part of mixture is taken out and replaced by water and this process is further repeated 2 times more, find the quantity of mix replaced.
एक बर्तन में दूध और पानी के बीच का अंतिम अनुपात 64 : 61 है। यदि प्रारंभ में 100 लीटर दूध था। मिश्रण के कुछ हिस्से को निकाल लिया जाता है और पानी से बदल दिया जाता है और इस प्रक्रिया को आगे 2 बार और दोहराया जाता है, तो प्रतिस्थापित मिश्रण की मात्रा ज्ञात कीजिए।
Option “A” is correct.
If a container contains x units of a liquid from which y units are taken out and replaced by water. After n such operations, quantity of liquid in final mixture will be.
Quantity of liquid in final Mixture = x × (1−y/x)n units
In final mixture,
⇒ 64 = 125 × (1−y/100)3
⇒ ∛(64/125) = (1−y/100)
⇒ 4/5 = (1−y/100)
⇒ y/100 = 1/5
⇒ y = 20 litres
∴ The quantity of mix replaced is 20 litres.
2. In a mixture of salt and water; salt is 15%. If some salt is added into the mixture then salt becomes 25% and the Final quantity of the mixture becomes 102L; Find the initial quantity of the mixture?
नमक और पानी के मिश्रण में; नमक 15% है। यदि मिश्रण में कुछ मात्रा में और नमक डाला जाता है तो यह नमक 25% हो जाता है और मिश्रण की अंतिम मात्रा 102 लीटर हो जाती है; मिश्रण की प्रारंभिक मात्रा ज्ञात कीजिये?
Option “D” is correct.
Let the initial Quantity of mixture be “x”
Initial Ratio of Salt to Water = 15 : 85 = 3 : 17
Final Ratio of Salt to Water = 25 : 75 = 1 : 3
According to question, the quantity of water remains the same
Thus, initial and final ratios become
Initial Ratio of Salt to Water = 9 : 51
Final Ratio of Salt to Water = 17 : 51
Total units in final mixture = 68 units = 102 L
Initial units of mixture = 9 + 51 = 60 units
Initial Quantity of mixture = 60 × (102/68)
∴ Initial Quantity of mixture = 90 L
3. A milkman uses three containers for selling milk, their capacities being 40 L, 30 L and 20 L respectively. He fills respectively 87.5%, 80% and 90% of the containers with a mix of milk and water in the ratios, 3 : 2, 5 : 1 and 7 : 2 respectively. What is the ratio of the total quantity of milk to that of water carried by him?
एक दूध वाला दूध बेचने के लिए तीन बर्तन का उपयोग करता है जिनकी क्षमता क्रमशः 40 ली, 30 ली और 20 ली है। वह बर्तन के क्रमशः 87.5%, 80% और 90% भाग को क्रमशः 3 : 2, 5 : 1 और 7 : 2 के अनुपात में दूध और पानी के मिश्रण से भरता है। उसके पास दूध और पानी की कुल मात्रा का अनुपात क्या है?
Option “C” is correct.
The quantity filled in container 1 = 40 × 87.5/100 = 35 L
The quantity filled in container 2 = 30 × 80/100 = 24 L
The quantity filled in container 3 = 20 × 90/100 = 18 L
The quantity of milk in container 1 = 35 × 3/5 = 21 L
The quantity of milk in container 2 = 24 × 5/6 = 20 L
The quantity of milk in container 3 = 18 × 7/9 = 14 L
The quantity of water in container 1 = 35 × 2/5 = 14 L
The quantity of water in container 2 = 24 × 1/6 = 4 L
The quantity of water in container 3 = 18 × 2/9 = 4 L
4. A shopkeeper purchased two varieties of sugar costing Rs 40/kg and Rs 50/kg. 40 kg of first variety is mixed with 40 kg sugar of other variety and mixture is sold at Rs 54/kg. Find the profit percent earned in this transaction.
एक दुकानदार ने 40 रुपये किलो और 50 रुपये किलो मूल्य की चीनी की दो किस्में खरीदीं। पहली किस्म की 40 किलोग्राम चीनी को दूसरी किस्म की 40 किलोग्राम चीनी के साथ मिलाया जाता है और मिश्रण को 54 रुपये किलो के मूल्य पर बेचा जाता है। इस लेनदेन में अर्जित लाभ प्रतिशत ज्ञात कीजिये।
Option “B” is correct.
⇒ Cost price of mixture of sugar = [(40 × 40) + (40 × 50)]/(40 + 40)
5. A milkman gets the order to supply 500 litres of pure milk in the party. Instead of supplying pure milk he mixes 30% of the water in the milk. Further the order is increased by 10% and instead of mixing milk he again mixes the water. If the cost of 1 litre of milk is Rs. 40 and he sold the milk to the party at the rate of Rs. 50 per litre, then what is the overall profit made by the milkman?
एक दूधवाले को पार्टी में 500 लीटर शुद्ध दूध की आपूर्ति करने का ऑडर मिलता है। शुद्ध दूध की आपूर्ति के बजाय वह दूध में 30% पानी मिलाता है। इसके अलावा ऑडर में 10% की वृद्धि हुई है और दूध को मिलाने के बजाय वह फिर से पानी मिलाता है। यदि 1 लीटर दूध की लागत 40 रु. है और उन्होंने पार्टी को 50 रु. की दर से दूध बेचा। तो दूध वाले द्वारा किया गया समग्र लाभ क्या है?
Option “D” is correct.
According to the question he mixes 30% of the water in the milk
Quantity of milk sold = (70/100) × 500 = 350 litres
Cost of 350 litres of milk = 40 × 350 = Rs. 14000
The order is increased by 10% and he mixes water in it
Water added = (10/100) × 500 = 50 litres
Effective quantity of mixture sold = 500 + 50 = 550 litres
Price charged = 550 × 50 = Rs. 27500
Profit = 27500 – 14000 = Rs. 13500
6. Raman purchased two different kinds of milk. In the first mixture, the ratio of milk and water is 3: 4 and in the second mixture, it is 5: 6. If he mixes the two given mixture and makes the mixture of 36 litres in which the ratio of milk and water is 4: 5, find the quantity of the first mixture that is required to make the third mixture.
रमन दो अलग-अलग प्रकार के दूध खरीदता है। पहले मिश्रण में, दूध और पानी का अनुपात 3 : 4 है और दूसरे मिश्रण में यह 5 : 6 है। यदि वह दो दिए गए मिश्रण को मिलाता है और 36 लीटर का मिश्रण बनाता है जिसमें दूध और पानी का अनुपात 4 : 5 है, तो तीसरे मिश्रण को बनाने के लिए आवश्यक पहले मिश्रण की मात्रा ज्ञात कीजिये।
Option “C” is correct.
Using alligation
5/11 – 4/9 : 4/9 – 3/7
⇒ ((45 – 44) /99) : ((28 – 27)/63)
⇒ (1/99) : (1/63)
⇒ 7 : 11
⇒ 36 × (7/18) = 14 liters
7.What amount of rice at the price of 45 per kg should be added to another variety of 1 kg of rice costing Rs 80 per kg so that the mixture is sold at Rs. 60 per kg and the profit is 20%?
45 रु. प्रति किग्रा मूल्य के चावल की कितनी मात्रा 80 रु. प्रति किग्रा चावल की एक दूसरी किस्म के 1 किग्रा में मिलाया जाना चाहिए ताकि मिश्रण को 60 रु. प्रति किग्रा पर बेचा जाए और लाभ 20% हो?
Option “B” is correct.
let x amount of rice to be added,
Selling price = 60, profit = 20%,
cost price = 60 × 100/120 = 50
⇒ (80 – 50)/(50 – 45) = x/1
⇒ 30/5 = x/1
⇒ 6/1 = x/1
⇒ x = 6 kg
∴ The required quantity is 6 kg.
8. A 400 gram mixture contains 30% zinc, 45% iron and the remaining copper, so how many grams of copper will be in a 400 gram mixture?
एक 400 ग्राम मिश्रण में 30% जस्ता 45% लोहा तथा शेष तांबा है, तो 400 ग्राम मिश्रण में तांबा कितने ग्राम होगा?
Option “B” is correct.
Percentage of copper in mixture = 100% – (Zinc percentage in mixture + Iron percentage in the mixture)
⇒ Required percentage = 100% – (30% + 45%)
⇒ Required percentage = 25%
Weight of copper = Copper percentage in mixture × Total weight of the mixture
⇒ Required weight = 25% × 400
⇒ Required weight = 25/100 × 400
⇒ Required weight = 100 grams
∴ There are 100 grams of copper in the mixture.
9. In 225 L mixture of milk & water; The ratio of milk and water is 4 : 1. The quantity of water required to make the ratio of milk & water 3 : 1 is
दूध और पानी के 225 लीटर के मिश्रण में दूध और पानी का अनुपात 4:1 है। तो दूध और पानी का अनुपात 3 : 1 बनाने के लिए आवश्यक पानी की मात्रा क्या है?
Option “D” is correct.
Initially,
Milk = 225 × (4/5) = 180 L
Water = 225 × (1/5) = 45 L
Now,
Assume x liters of water is added
180/(45 + x) = 3/1
⇒ 60/(45 + x) = 1
⇒ 60 = 45 + x
⇒ x = 15
∴ Water added = 15 litres
10. In a mixture of sugar and water; Sugar is 32% If 14 litre of sugar is added then sugar becomes 40%; Find initial quantity of the Mixture?
चीनी और पानी के मिश्रण में; चीनी 32% है यदि 14 लीटर इसमें और मिलाई जाती है, तो चीनी की मात्रा इसमें 40% हो जाती है; मिश्रण की प्रारंभिक मात्रा ज्ञात कीजिये?
Option “C” is correct.
Let the initial Quantity of mixture be “x”
Initial Ratio of Sugar to Water = 32 : 68 = 8 : 17
Final Ratio of Sugar to Water = 40 : 60 = 2 : 3
According to question, the quantity of water remains the same
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