>> Aptitude >> Linear Equations

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Contents:

- Aptitude
- Approximation
- Average
- Boat and Stream
- Compound interest
- Discount
- Linear Equations
- Mensuration
- Mixture and Allegation
- Number series
- Number System
- Partnership
- Percentage
- Permutation and combination
- Pipes and Cisterns
- Probability
- Problem on ages
- Profit and Loss
- Ratio and Proportions
- Simple and compound interest
- Time and Distance
- Time and work
- Trains
- Unitary Method
- Word problems
- Work and Wages

1). 2x + 3y = 29 and y = x + 3, what is the value of x?
2x+3y = 29 ...(i) and y = x+3 ...(ii) Putting the value of y from Eq. (i) to Eq. (ii), we get 2x+3y = 29 \( \Large 2x+3 \left(x+3\right)=29 \) 2x+3x+9 = 29 = 5x = 20 Therefore, x = 4 | ||||

2). Deepak has some hens and some goats. If the total number of animal heads is 90 and the total number of animal feet is 248, what is the total number of goats Deepak has?
Let hens = H, goats = G -2G = -68 | ||||

3). The sum of the two digits is 15 and the difference between them is 3. What is the product of the digits?
Let the number be x and y. | ||||

4). The cost of 21 pencils and 9 clippers is Rs.819. What is the total cost of 7 pencils and 3 clippers together?
Let cost of 1 pencil and 1 clipper be p and c, respectively Now. according to the question, \( \Large 21p + 9c = Rs.819 \) \( \Large 3 \left(7p+3c\right)= Rs.819 \) \( \Large 7p + 3c = Rs.273 \) Cost of 7 pencils and 3 clippers = Rs.273. | ||||

5). The value of k for which kx+ 3y-k+ 3=0 and 12x+ky=k, have infinite solutions, is
For infinite solution \( \Large \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}} \) = \( \Large \frac{K}{12}=\frac{3}{K}=\frac{-K+3}{-K} \) = \( \Large \frac{K}{12}=\frac{3}{K}=K^{2}=36 \) Therefore, \( \Large K = \sqrt{36} = 6 \) | ||||

6). In a rare coin collection, there is one gold coin for every three non-gold coins. 10 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1 : 2. Based on the information; the total number of coins in the collection now becomes.
Let the number of gold coins initially be x and the number of non-gold coins be y. According to the question, 3x = y When 10 more gold coins, total number gold coins become x + 10 and the number non-gold coins remain the same at y. Now, we have \( \Large 2 \left(10+x\right)=y \) Solving these two equations, we get x = 20 and y = 60. Total number of coins in the collection at the end is equal to x+10+y = 20+10+60 = 90. | ||||

7). If \( \Large \frac{\sqrt{3+x}+\sqrt{3-x}}{\sqrt{3+x}-\sqrt{3-x}}=2 \), then x is equal to
Given, \( \Large \frac{\sqrt{3+x}+\sqrt{3-x}}{\sqrt{3+x}-\sqrt{3-x}}=2 \) | ||||

8). In an examination, a student scores 4 marks for every correct answer and losses 1 mark for every wrong answer. A student attempted all the 200 questions stud and scored 200 marks. Find the number of questions he answered correctly.
Let the number of correct answers be x and number of wrong answers be y Then, 4x - y = 200 ...(i) and x + y = 200 ...(ii) On adding Eqs. (i) and (ii). we get 4x - y = 200 x + y = 200 5x = 400 Therefore, x = 80 | ||||

9). The graphs of ax + by = c, dx + ey = f will be I. parallel, if the system has no solution. II. coincident, if the system has finite numbers of solutions. III. intersecting, if the system has only one solution. Which of the above statements are correct?
ax + by = c and dx + ey = f | ||||

10). If \( \Large 3^{x+y}=81 \) and \( \Large 81^{x-y}=3 \), then what is the value of x?
Given, \( \Large 2x = \frac{17}{4} = x = \frac{17}{8} \) |