Statement Sums involving Linear Equations
Statement Sums involving Linear Equations
Statement Sums involving Linear Equation: In these sums a certain situation is given we have to analyse the statement and then suppose a certain quantity. and will then try to identify a relation with the quantity we have supposed.
The procedure to translate a word problem in the form of an equation is known as the formulation of the problem. Thus, the process of solving a word problem consists of two parts, namely, formulation and solution.
The following steps should be followed to solve a word problem:
Step I Read the problem carefully and note what is given and what is required.
Step II Denote the unknown quantity by some letters, say x, y, z, etc.
Step III Translate the statements of the problem into mathematical statements.
Step IV Using the condition (s) given in the problem, form the equation
Step V Solve the equation for the unknown.
Step VI Check whether the solution satisfies the equation.
Example: The numerator of a fraction is 4 less than the denominatr. If 1 is added to both its numerator and denominator, it becomes 1/2. FInd the fraction.
Solution Let the denominator of the fraction be x. Then,
Numerator of the fraction = x - 4
Fraction
If 1 is added to both its numerator and denominator, the fraction becomes .
[ Using cross - multiplication]
Putting x = 7 in (i), we get
Fraction Hence, the given fraction is
Example : How much pure alcohol be added to 400 ml of a 15% solution to make its strength 32%?
Solution Let x ml pure alcohol be added to 400 ml of a 15% solution to make its strength 32%. Here, 15% solution means that there is 15 ml pure alcohol in a solution of 100 ml.
Now, Quantity of alcohol in 100 ml solution = 15 ml
Quantity of alcohol in one ml solution
Quantity of alcohol in 400 ml solution
Total quantity of the solution = (400 + x) ml
Total quantity of alcohol in (400 + x) ml solution = (60 + x) ml
Quantity of alcohol in one ml
Quantity of alcohol in 100 ml
Strength of the solution
100%
But, the strength of the solution is given as 32%.
[ Multiplying both sides by (400 + x)]
Thus, 100 ml alcohol must be added to make 32% strength of the solution.
Find two consecutive even numbers such that smaller of the two numbers is | |||
| Right Option : D | |||
| View Explanation | |||
One-sixth of a number when subtracted from the number itself gives 25. The number is __________________________ | |||
| Right Option : A | |||
| View Explanation | |||
Two numbers are in the ratio 5:6. If 8 is subtracted from each, the ratio becomes 4:5. Find the numbers. | |||
| Right Option : D | |||
| View Explanation | |||
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