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TEST OF QUANTITATIVE APTITUDE
The Quantitative Aptitude Section of Success Bureau Study Material covers the complete syllabus and includes Often Asked Questions
( OAQs) in the Competitive Examinations .
Hence, you are advised to properly cram the contents . You should not waste time in learning out dated books .
Below is given a small Sample of the Study Material provided to the students .
RATIO & PROPORTION
The number of times one quantity contains another quantity of the same kind is called the ratio of the two quantities .
Clearly, a ratio may be expressed in the form of a fraction. A ratio, for example, of Rs.5/- and Rs. 7/- may be expressed either in the form 5 : 7 or in the form 5 / 7.
Proportion is an equality of ratios . For example, 15 : 45 = 1 : 3 or 15/45 = 1/3 .
Each of these expressions indicates a proportional.
The terms 15 , 45, 1, 3 are distinguished as the 1st , 2nd , 3rd and 4th proportional respectively.
The Ist and 4th proportional are called ‘Extremes’ . The 2nd and 3rd proportional are called the ‘Means’ .
In the above proportional, it is clear that 15 x 3 = 45 x 1
i.e. Product of the extremes = Product of the means
Examples :
Q.1 Find a fourth proportional to the numbers 6, 8, 9 .
Solution : If X be the fourth proportional, then 6 : 8 = 9 : X
Or 6X = 8 x 9 ( By Cross multiplication ) X = 8 x 9/6 Or X = 12
Q.2 If 3 : 8 = 6 : X, then X = ?
Solution : X = 8 x 6 / 3 = 16
Q.3 Find the fourth proportional to 6, 18.
Solution : Here, we would have to find out a fourth proportional to 6,18,18.
So, if X be the fourth proportional , then , 6 : 18 = 18 : X
Hence , X = 18 x 18 / 6 = 54 .
Q.4 Find the mean proportional between 8 and 2.
Solution : If X be the required mean proportional , then 8 : X : : X : 2 ( Multiply Means & Extremes )
Hence , X = 4
Q.5 If 12 : X = X : 3, then X = ?
Solution : X . X = 12×3 = 36 , Hence, X = 6
Q.6 If 15 boys can do a piece of work in 120 days, in how many days will 18 boys do it ?
Solution ( SHORT CUT ) : Since the number of “boys days” required to complete any piece of work is always the same, so :
The number of boys x The number of days in Ist case
= The number of boys x The number of days in 2nd case
Hence, 15 x 120 = 18 x X or X = 100 days
Q.7 If 12 men working 4 hours a day for 120 days can complete a piece of work, how many men working 6 hours a day for 12 days will be needed ?
Solution ( SHORT – CUT ) : Since the number of “ man day hours” need to complete the work in both the cases is the same so, 12 X 4 X 120 = X x 6 X 12 or X = 80 men
Q.8 If 8 men reap 40 acres in 12 days, how many acres
will 6 men reap in 10 days.
Solution ( SHORT – CUT ) : Since the “man days” required per unit of work is always the same, so :
Men 1 x Time / Work 1 = Men 2 x Time / Work 2
So, 8 x 12 / 40 = 6 x 10 / X ( Cross Multiplication ) Or X = 25 acres
Q.9 If Rs. 16,000 maintain a family of 4 persons for 60 days, how long will Rs. 21,000 maintain a family of 7 persons ?
Solution ( SHORT – CUT ) : 4 x 60 / 16,000 = 7x X/21,000 Or X = 45 days .
Q.10 If 9 men or 15 women can do a piece of work in 30 days, in how many days can the work be done by 6 men and 20 women working together ?
Solution : Since , 9 M = 15 W
M = 15 W /9 ; 6M = 15W/9 x 6 10 W . Now, 6 M + 20 W = 10 W + 20 W = 30 Women
Now, we have to find out that if 15 women can do a work in 30 days, then 30 women can do the same job in how many days ?
The proportion becomes , 30 : 15 = 30 : X Or X = 30 x 15 / 30 = 15 days
Q.11 If 1/18 : X = 9 : 4 , find the value of X .
Solution : 1/18 : X = 9 : 4 or 9X = 1/18 x 4 Or X= 4 / 18 x 9 = 2 / 81
Special Note
The Quantitative Aptitude Section of Success Bureau Study Material covers complete syllabus and includes Often Asked Questions ( OAQs) in the Competitive Examinations .
Hence, you are advised to properly cram the contents . You should not waste time in learning out dated books .
Above is given a small sample of the Study Material provided to the students .