A manufacturer has 600 litres of a 12% solution of acid. How many litres
of a 30% acid solution must be added to it so that acid content in the resulting mixture
will be more than 15% but less than 18%?
In an experiment, a solution of hydrochloric acid is to be kept between
30° and 35° Celsius. What is the range of temperature in degree Fahrenheit if conversion
formula is given by C =
5
9
(F – 32), where C and F represent temperature in degree
Celsius and degree Fahrenheit, respectively
Solve the system of inequalities:
3x – 7 < 5 + x ... (1)
11 – 5 x ≤ 1 ... (2)
and represent the solutions on the number line.
A man wants to cut three lengths from a single piece of board of length 91cm.
The second length is to be 3cm longer than the shortest and the third length is to
be twice as long as the shortest. What are the possible lengths of the shortest
board if the third piece is to be at least 5cm longer than the second?
[Hint: If x is the length of the shortest board, then x , (x + 3) and 2x are the
lengths of the second and third piece, respectively. Thus, x + (x + 3) + 2x ≤ 91 and
2x ≥ (x + 3) + 5].
The longest side of a triangle is 3 times the shortest side and the third side is 2 cm
shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find
the minimum length of the shortest side
Find all pairs of consecutive even positive integers, both of which are larger than
5 such that their sum is less than 23.
Find all pairs of consecutive odd positive integers both of which are smaller than
10 such that their sum is more than 11
To receive Grade ‘A’ in a course, one must obtain an average of 90 marks or
more in five examinations (each of 100 marks). If Sunita’s marks in first four
examinations are 87, 92, 94 and 95, find minimum marks that Sunita must obtain
in fifth examination to get grade ‘A’ in the course
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