31. The cost of rice A is Rs. 24 per kg and the cost of rice B is Rs. x. 30 kg of rice A and 20 kg of rice B was mixed and sold at a profit of 50% at a rate of Rs. 43.2 per kg. Find the value of x.
चावल A का क्रय मूल्य 24 रुपये प्रति किलोग्राम है और चावल B का क्रय मूल्य x रुपये है। 30 किलो चावल A और 20 किलो चावल B को आपस में मिलाया जाता हैं और इसको 50% के लाभ पर 43.2 रुपये प्रति किलोग्राम की दर से बेचा जाता है। x का मान ज्ञात कीजिए?
Option “C” is correct.
∵ The selling price of rice = Rs. 43.2 per kg
∴ The cost price of rice = 43.2 × 100/150 = Rs. 28.8 per kg
⇒ The cost price of 50 kg = 28.8 × 50 = Rs. 1440
According to question
⇒ 24 × 30 + 20 × x = 1440
⇒ x = Rs. 36
32. In what ratio should cement costing Rs. 250 per bag be mixed with cement costing Rs. 325 per bag so that the cost of the mixture is Rs. 300 per bag. (A bag of cement is 50 kg).
250 रुपये प्रति बैग वाली सीमेंट को, 325 रुपये प्रति बैग वाली सीमेंट के साथ किस अनुपात में मिलाया जाए कि मिश्रण की लागत 300 रुपये प्रति बैग आए (सीमेंट का एक बैग 50 किग्रा का है)।
Option “A” is correct.
Let the number of bags be x costing per bag Rs 250
Let the number of bags be y costing per bag Rs 325
Total cost of x bags = x × 250 = 250x
Total cost of y bags = y × 325 = 325y
According to the question
(250x + 325y)/(x + y) = 300
⇒ x/y = 1/2
∴ ratio of bag costing 250 to the bag cost 325 is 1 : 2
33. The ratios of acid and water in vessels A and B are 4 : 5 and 7 : 5, respectively. In what ratio should the contents of A and B be mixed to get a solution containing 50% acid?
पात्र A और B में एसिड और पानी का अनुपात क्रमशः 4 : 5 और 7 : 5 है। 50% एसिड युक्त विलयन प्राप्त करने के लिए A और B की सामग्री को किस अनुपात में मिश्रित किया जाना चाहिए?
Option “C” is correct.
The ratio of acid to water in vessel A is 4 : 5
Let the total volume of acid and water be 4x and 5x
The ratio of acid to water in vessel B is 7 : 5
Let the total volume of acid and water be 7y and 5y
According to the question volume of water and acid must be equal
So,
(4x + 7y) : (5x + 5y) = 1 : 1
⇒ x = 2y
Putv value of x = 2y to get volume
Volume of vessel A = 4x + 5x = 9x
⇒ 18y
Volume of vessel B = 7y + 5y
⇒ 12y
Ratio of vessel A to B
Volume of vessel A : Volume of vessel B = 18y : 12y
⇒ 3 : 2
∴ 3 : 2 will be the ratio at which vessel A and B must be mixed
34. A vendor bought two varieties of tea, brand A and brand B, costing Rs. 15 per 100 g and Rs. 18 per 100 g, respectively, and mixed them in a certain ratio. Then, he sold the mixture at Rs. 20 per 100 g, making a profit of 20%. What was the ratio of brand A to brand B tea in the mixture?
एक विक्रेता ने दो प्रकार की चाय ब्रांड A और ब्रांड B को खरीदा, जिसका क्रय मूल्य क्रमशः 15 रुपये प्रति 100 ग्राम और 18 रुपये प्रति 100 ग्राम हैं, और उन्हें एक निश्चित अनुपात में मिलाया। उन्होंने इस मिश्रण को 20 रुपये प्रति 100 ग्राम बेचकर 20% का लाभ कमाया। मिश्रण में ब्रांड A से ब्रांड B चाय का अनुपात क्या था?
Option “A” is correct.
Let x gram of brand A and y gram of brand B is mixed.
For 100g brand A costs Rs. 15
For x g brand A will cost 15x/100
For 100g brand B costs Rs. 18
For y g brand B will cost 18x/100
So, the total cost price for (x + y) grams is
⇒ x + y = 15x/100 + 18y/100 —-(i)
Sold at Rs. 20 with 120% profit, Cost price will be
⇒ 100% = (20/120) × 100 = Rs. 100/6
Cost price for 100g is Rs. 100/6,
Now find cost price for (x + y) grams
⇒ x + y = (100/6) × {(x + y)/100}
⇒ x + y = (x + y)/6
Put value of equation(i)
⇒ 15x/100 + 18y/100 = (x + y)/6
⇒ 90x + 108y = 100x + 100y
⇒ 8y = 10x
⇒ x/y = 8/10 = 4/5
∴ The ratio of the mixture of Brand A and B is 4 : 5
35. A solution of milk and water contains milk and water in the ratio of 3 : 2. Another solution of milk and water contains milk and water in the ratio of 2 : 1. Forty litres of the first solution is mixed with 30 litre of the second solution. The ratio of milk and water in the resultant solution is:
दूध और पानी के एक मिश्रण में दूध और पानी 3 : 2 के अनुपात में है। दूध और पानी के एक और मिश्रण में दूध और पानी 2 : 1 के अनुपात में है। पहले मिश्रण के चालीस लीटर को दूसरे मिश्रण के 30 लीटर के साथ मिश्रित किया जाता है। परिणामी मिश्रण में दूध और पानी का अनुपात है:
Option “A” is correct.
Volume of milk in first solution = (3/5) × 40 liters
⇒ 24 liters
Volume of water in first solution = (2/5) × 40 liters
⇒ 16 liters
Volume of milk in second solution = (2/3) × 30 liters
⇒ 20 liters
Volume of water in second solution = (1/3) × 30 liters
⇒ 10 liters
Volume of milk in new mixture = Volume of milk in first solution + Volume of milk in second solution
⇒ (24 + 20) liters
⇒ 44 liters
Volume of water in new mixture = Volume of water in first solution + Volume of water in second solution
⇒ (16 + 10) liters
⇒ 26 liters
Ratio of milk and water in mixture = 44/26
⇒ 22/13
⇒ 22 : 13
∴ The ratio of milk and water in the resultant solution is 22 : 13
36. A container contains 20 L mixture in which there is 10% sulphuric acid. Find the quantity of sulphuric acid to be added in it to make the solution to contain 25% sulphuric acid.
एक पात्र में 20 लीटर का मिश्रण है जिसमें 10% सल्फ्यूरिक अम्ल है। ज्ञात कीजिए कि सल्फ्यूरिक अम्ल की कितन मात्रा जोड़ने पर मिश्रण को 25% सल्फ्यूरिक अम्ल युक्त घोल बनाया जा सकता है।
Option “B” is correct.
According to the question
The quantity of Sulphuric acid in the mixture is
⇒ 20 × 10%
⇒ 2 L
The remaining quantity in the mixture is
⇒ 20 – 2
⇒ 18 L
After, adding Sulphuric acid to the mixture, the remaining quantity becomes 75% of the mixture, then
The whole quantity of the mixture is
⇒ 18 × 100/75
⇒ 24 L
Now,
In the mixture, the quantity of Sulphuric acid is
⇒ 24 × 25%
⇒ 6 L
The quantity of Sulphuric acid added to the mixture is
⇒ 6 – 2
⇒ 4 L
∴ The quantity of Sulphuric acid is added to the mixture is 4 L.
37.In what ratio should sugar costing Rs. 40 per kg be mixed with sugar costing Rs. 48 per kg , so as to earn a profit of 20% by selling the mixture at Rs. 54 per kg?
किस अनुपात में चीनी को 40 रुपये प्रति किलोग्राम और चीनी को 48 रुपये प्रति किलोग्राम के हिसाब से मिलाया जाना चाहिए, ताकि मिश्रण को 54 रुपये प्रति किलोग्राम के हिसाब से बेचकर 20% का मुनाफा कमाया जा सके?
Option “C” is correct.
Let the cost price of whole mixture be Rs. x.
⇒ x = 54 × 100/120
⇒ x = Rs. 45
Ratio = (48 – 45) ∶ (45 – 40)
⇒ 3 ∶ 5
∴ The ratio is 3 : 5.
38. In a mixture of 60 litres, milk and water are in the ratio 2 : 1. Find the quantity of water to be added to make the ratio 4 : 3
60 लीटर के मिश्रण में, दूध और पानी 2 : 1 के अनुपात में हैं। 4 : 3 का अनुपात बनाने के लिए मिलाए जाने वाले पानी की मात्रा ज्ञात कीजिये।
Option “B” is correct.
⇒ In the Mixture of 60 liter = milk + water = 2 + 1 unit = 3 unit
⇒ 3 unit = 60 liter
⇒ 1 unit = 20 liter
⇒ Milk: Water = 2 × 20: 1 × 20 = 40 : 20
Now as given to make the ratio of Milk: Water = 4 : 3 by adding X liter of water
⇒ 40/(20 + X ) = 4/3
⇒ 40 × 3 = 4 × ( 20 + X )
⇒ 120 = 80 + 4X
⇒ 4X = 40
∴ X = 10
39. Two alloys A and B contain copper and zinc in the ratio 7 : 2 and 5 : 3 respectively. How many kg of A and B must be melted in order to get an alloy of 44 kg containing copper and Zinc in the ratio 3 : 1?
दो मिश्रधातु A और B में क्रमशः 7 : 2 और 5 : 3 के अनुपात में तांबा और जस्ता है। 3 : 1 के अनुपात में तांबा और जस्ता युक्त 44 किलोग्राम मिश्रधातु प्राप्त करने के लिए A और B की कितनी किलोग्राम मात्रा को पिघलाया जाना चाहिए?
Option “D” is correct.
Let x liters is added from alloy A and y liters is added from alloy B.
Then (7x/9) + (5y/8) / (2x/9) + (3y/8) = 3 / 1
⇒ (7x/9) + (5y/8) = (6x/9) + (9y/8)
⇒ [(7x-6x)/9] = [(9y-5y)/8]
⇒ (x/9) = (4y/8)
⇒ (x/y) = (9/2)
⇒ x : y = 9 : 2
Quantity taken from alloy A = (44/11) × 9
⇒ 4 × 9
⇒ 36 kg
Quantity taken from alloy B = (44/11) × 2
⇒ 4 × 2
⇒ 8 kg
∴ 36 kg added from alloy A and 8 kg added from alloy B
40. An alloy X contains by weight copper and tin in the ration 7 : 3 and alloy Y contain copper and tin in the ratio 3 : 2. X and Y are taken in the ratio 4 : 1 and melted to form alloy Z. The percentage of copper in alloy Z is:
एक मिश्रधातु X में भार के अनुसार तांबे और टिन का अनुपात 7 : 3 है और मिश्रधातु Y में तांबे और टिन का अनुपात 3 : 2 है। X और Y को 4 : 1 के अनुपात में लिया जाता है और मिश्रधातु Z बनाने के लिए पिघलाया जाता है। मिश्रधातु Z में तांबे का प्रतिशत है:
Option “D” is correct.
Quantity of copper in 10units of X = 7units
Similarly, Quantity of copper in 10units of Y = 6units
To form Z, we need X : Y = 4 : 1
∴ 40units of X contains 28 units copper and 10units of Y contains 6units copper
∴ in total 50units, copper is 34units required % = (34/50) × 100 = 68%
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