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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

**S**pecial 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 .