Ps problems

Question

ques 1

1
--------
1/0.03+1/0.37

ques 2 solution y is 30% liquid x and 70 % water. If 2 Kg of water evaporates from 8 kilogram of solution y and 2 killogram of solution y are added to the remaining 6 kg of liquid, what percent of this new solution is liquid X?

que3 If x Not equal to zero and x = square root of 4xy-4y^2, then in terms of y, x=?

ques 4 After paying a 10% tax on all income over 3000, a peter had net incomeof 12000. what is was the income before taxes?

ques 5 A certain elevator has a safe weiight limit of 2000pounds. What is great possible number of people who can safely ride on the elevator at one time with average weight of half the riders being 180 pounds and the average weight of others being 215 pounds?

Ques 5 If each side of Triangle ACD has lenghth 3 and if ad has length = 1, what is are of BCDE if a perpendicular is dropped from sides of traingle.

Anurag@Gurome · Answer

alltimeacheiver wrote:ques 1

1
--------
1/0.03+1/0.37

This problem is not clear.
If it asking to determine the value of 1/[(1/0.03) + (1/0.37)], then we can proceed as follows.

.. 1/[(1/0.03) + (1/0.37)]
= 1/[(0.03+0.37)/(0.03)*(0.37)]
= (0.03)*(0.37)/(0.03 + 0.37)
= (0.0111)/(0.40)
= 111/4000
= 111/(4*1000)
= (27.75/1000)
= 0.02775

Anurag@Gurome · Answer

alltimeacheiver wrote:2. Solution y is 30% liquid x and 70 % water. If 2 Kg of water evaporates from 8 kilogram of solution y and 2 kilogram of solution y are added to the remaining 6 kg of liquid, what percent of this new solution is liquid x?

Amount of liquid x in 8 kg of solution y = (30% of 8) kg = 2.4 kg

Amount of liquid x in 2 kg of solution y = (30% of 2) kg = 0.6 kg

Hence, amount of liquid x in new solution = (2.4 + 0.6) kg = 3 kg
And, total amount of new solution = (8 - 2 + 2) kg = 8 kg

Therefore, required percentage = (3/8)*100 = 37.50

Anurag@Gurome · Answer

alltimeacheiver wrote:3. If x ≠ 0 and x = √(4xy - 4y²), then in terms of y, x = ?

=> x = √(4xy - 4y²)
=> x² = (4xy - 4y²) ................. Squaring both sides
=> (x² - 4xy + 4y²) = 0
=> (x - 2y)² = 0
=> x = 2y

Anurag@Gurome · Answer

alltimeacheiver wrote:4. After paying a 10% tax on all income over 3000, Peter had net income of 12000. What was his income before taxes?

Say his, income before taxes was 100x.
Hence, his income tax = 10% of (100x - 3000) = (10x - 300)
Hence, net income after paying taxes = 100x - (10x - 300) = (90x + 300)

Therefore, (90x + 300) = 12000
=> 90x = 11,700
=> 100x = 10*11,700/9 = 13,000

His income before taxes was 13000.

rohu27 · Answer

one small req. can u plz mention th source of the questions along wth ur posts, as people like me wouldnt want to do questions from some CAT's we havet taken yet.

thanks.

alltimeacheiver wrote:ques 1

1
--------
1/0.03+1/0.37

ques 2 solution y is 30% liquid x and 70 % water. If 2 Kg of water evaporates from 8 kilogram of solution y and 2 killogram of solution y are added to the remaining 6 kg of liquid, what percent of this new solution is liquid X?

que3 If x Not equal to zero and x = square root of 4xy-4y^2, then in terms of y, x=?

ques 4 After paying a 10% tax on all income over 3000, a peter had net incomeof 12000. what is was the income before taxes?

ques 5 A certain elevator has a safe weiight limit of 2000pounds. What is great possible number of people who can safely ride on the elevator at one time with average weight of half the riders being 180 pounds and the average weight of others being 215 pounds?

Ques 5 If each side of Triangle ACD has lenghth 3 and if ad has length = 1, what is are of BCDE if a perpendicular is dropped from sides of traingle.

Anurag@Gurome · Answer

alltimeacheiver wrote:5. A certain elevator has a safe weight limit of 2000 pounds. What is largest possible number of people who can safely ride on the elevator at one time with average weight of half the riders being 180 pounds and the average weight of others being 215 pounds?

Say, the largest number of riders is 2x.
Hence, total weight of the riders = (Total weight of the riders with average weight 180 pounds) + (Total weight of the riders with average weight 215 pounds) = (180x + 215x) = 395x pounds

This must be less than 2000 pounds.
Hence, 395x < 2000 => x < (2000/395) = 5.(Something)

Hence, largest possible value of x is 5.
Therefore, the largest possible number of riders is 10.

Anurag Mairal, Ph.D., MBA
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Anurag@Gurome · Answer

alltimeacheiver wrote:6. If each side of Triangle ACD has lenghth 3 and if ad has length = 1, what is are of BCDE if a perpendicular is dropped from sides of traingle.

Please check the wordings of the problem.
"If each side of Triangle ACD has lenghth 3", then it is not possible that "ad has length = 1".

Also I think the original question is accompanied with an image or a declaration regarding position of point B.

ankur.agrawal · Answer

Anurag@Gurome wrote:alltimeacheiver wrote:4. After paying a 10% tax on all income over 3000, Peter had net income of 12000. What was his income before taxes? Say his, income before taxes was 100x. Hence, his income tax = 10% of (100x - 3000) = (10x - 300) Hence, net income after paying taxes = 100x - (10x - 300) = (90x + 300) Therefore, (90x + 300) = 12000 => 90x = 11,700 => 100x = 10*11,700/9 = 13,000 His income before taxes was 13000. Any specific reason for taking "income before taxes was 100x." I took x.

Anurag@Gurome · Answer

ankur.agrawal wrote:Any specific reason for taking "income before taxes was 100x." I took x.

Percentage problems with the principal value as unknown becomes easier to solve if we assume any multiple of 100 as the principal value. This is because it instantly converts any percentage, for example say 30% of principal value as 30x. You can always take x as the unknown. But sometimes taking multiple of 100 has its own advantages.

Although for this particular problem it doesn't make much difference whether you take 100x or x.

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