Quant Quiz - Part II

Directions (1- 5): The following pie-chart shows the sources of funds to be collected by the National Highways Authority of India (NHAI) for its Phase II projects. Study the pie-chart and answers the question that follow.

Sources of funds to be arranged by NHAI for Phase II projects (in Rs. crores)

1. Nearly about 20% of the funds are to be arranged through:

A. SPVS 

B. External Assistance

C. Annuity 

D. Market Borrowing

2. If NHAI could receive a total of Rs. 9695 crores as External Assistance, by what percent (approximately) should it increase the Market Borrowing to arrange for the shortage of funds?

A. 4.5 % 

B. 7.5 %

C. 6 % 

D. 8 %

3. If the toll is to be collected through an outsourced agency by allowing a maximum 10% commission, how much amount should be permitted to be collected by the outsourced agency, so that the project is supported with Rs. 4910 crores?

A. Rs. 6213 crores 

B. Rs. 5827 crores

C. Rs. 5401 crores 

D. Rs. 5316 crores

4. The central angle corresponding to Market Borrowing is

A. 52° 

B. 137.8°

C. 187.2° 

D. 192.4°

5. The approximate ratio of the funds to be arranged through Toll and that through Market Borrowing is

A. 2:1 

B. 1:6

C. 3:11 

D. 2:5

Directions (6 – 10): The following line graph gives the ratio of the amounts of imports by a company to the amount of exports from that company over the period from 1995 to 2001.

Ratio of Value of Imports to Exports by a Company over the Years.

6. If the imports in 1998 were Rs. 250 crores and the total exports in the years 1998 and 1999 together was Rs. 500 crores, then the imports in 1999 was?

A. Rs. 250 crores 

B. Rs. 300 crores

C. Rs. 357 crores 

D. Rs. 420 crores

7. The imports were minimum proportionate to the exports of the company in the year ?

A. 1995 

B. 1996

C. 1997 

D. 2000

8. What was the percentage increase in imports from 1997 to 1998?

A. 72 

B. 56

C. 28 

D. Data inadequate

9. If the imports of the company in 1996 was Rs. 272 crores, the exports from the company in 1996 was?

A. Rs. 370 crores 

B. Rs. 320 crores

C. Rs. 280 crores 

D. Rs. 275 crores

10. In how many of the given years were the exports more than the imports?

A. 1 

B. 2

C. 3 

D. 4

Answers:
1. Answer: (B)
20% of the total funds to be arranged = Rs. (20% of 57600) crores
= Rs. 11520 crores = Rs. 11486 crores. (Approx)
Rs. 11486 crores is the amount of funds to be arranged through External Assistance

2. Answer: (C)
Shortage of funds arranged through External Assistance = Rs. (11486 - 9695) crores
= Rs. 1791 crores.
Increase required in Market Borrowing = Rs. 1791 crores.
Percentage increase required = {[(1791 / 29952) ] x 100}% = 5.98%  = 6%. (Approx)

3. Answer: (C)
Amount permitted = (Funds required from Toll for projects of Phase II) + (10% of these funds)
= Rs. 4910 crores + Rs. (10% of 4910) crores
= Rs. (4910 + 491) crores
= Rs. 5401 crores.

4. Answer: (C)
Central angle corresponding to Market Borrowing =[(29952/57600)] x 360º = 187.2º

5. Answer: (B)
Required ratio = 4910/29952= 1/6.1 = 1/6 (Approx)

6. Answer: (D)
The ratio of imports to exports for the years 1998 and 1999 are 1.25 and 1.40 respectively.
Let the exports in the year 1998 = Rs. x crores.
Then, the exports in the year 1999 = Rs. (500 - x) crores.
1.25 = 250/x
x = 250 /1.25 = 200 ( Using ratio for 1998
Thus, the exports in the year 1999 = Rs. (500 - 200) crores = Rs. 300 crores.
Let the imports in the year 1999 = Rs. y crores.
Then, 1.40 = y / 300
y = ( 300 * 1.40 ) = 420
Imports in the year 1999 = Rs. 420 crores.

7. Answer: (C)
The imports are minimum proportionate to the exports implies that the ratio of the value of imports to exports has the minimum value.
Now, this ratio has a minimum value 0.35 in 1997, i.e., the imports are minimum proportionate to the exports in 1997.

8. Answer: (D)
The graph gives only the ratio of imports to exports for different years. To find the percentage increase in imports from 1997 to 1998, we require more details such as the value of imports or exports during these years.
Hence, the data is inadequate to answer this question.

9. Answer: (B)
Ratio of imports to exports in the year 1996 = 0.85.
Let the exports in 1996 = Rs. x crores.
Then, 272/x = 0.85
x = 272 / 0.85= 320
Exports in 1996 = Rs. 320 crores.

10. Answer: (D)
The exports are more than the imports imply that the ratio of value of imports to exports is less than 1.
Now, this ratio is less than 1 in years 1995, 1996, 1997 and 2000.

Thus, there are four such years.

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List of Common geometry formulas

Hello Readers,

           We are providing Here common geometry formulas for some basic shapes  because geometry is one of the most asked topic in ssc exams. If you have checked analysis for important topics for SSC CGL exam based on past 4 year of exam paper analysis. In last 2013 ssc cgl exam, there are 12 questions on Geometry subject, so you can no escape from this subject. We know its bit boring and difficult too but the thing is you need to crack this subject at any cost and for that reason, you need this formulas too.So Start preparation for the geometry subject for SSC exams. you can find the formulas on two dimension and three dimension figures. Like, formulas of Circle, Sector of circle, Segment of circle, Arc of circle, square, rectangle, rhombus, parallelogram, trapezoid, kite, triangle common, equilateral triangle, isosceles triangle, Prism, rectangular, cone, frustum of right circular cone, pyramid, frustum of pyramid, sphere, hemisphere, hollow­ cylinder etc.

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Quant Quiz For SSC

1. The average age of 40 boys in a class is 15. The average age of a group of 18 boys in the class is 16 and the average age of another12 boys in the class is 14. What is the average age of the remaining boys in the class?
(1) 15•25 years 
(2) 14.4 years
(3) 14•75 years 
(4) None of these

2. Ruby invested an amount of Rs. 5,800 for 2 years. At what rate of compound interest will she get an amount of Rs. 6394•5 at the end of two years ?
(1) 5 p.c.p.a.  
(2) 4 p.c.p.a.
(3) 6 p.c.p.a.  
(4) 8 p.c.p.a.

3. A boat covers a distance of 30 km downstream in 2 hours while it takes 6 hours to cover the same distance upstream. How much time the boat will take to cover 90 km in still water?
(1) 6 hrs  
(2) 9 hrs
(3) 15 hrs  
(4) None of these

4. A lent Rs 5000 to B for 2 years and Rs 3000 to C for 4 years on simple interest at the same rate of interest and received Rs 2200 in all from both of them as interest. The rate of interest is
(1) 5%  
(2) 7%
(3) 8%  
(4) None of these

5. Train A and B travel to a place at a speed of 35 and 55 km/h respectively. If car B takes 7/2  hours  less time than A for the journey, the distance of the place is_
(1) 300.25 km 
(2) 400 km
(3) 350.565 km 
(4) 336.875 km


6. Two numbers are such that if the first is subtracted from six times the second, their difference becomes 71, and if the second be added to 7 times the first , their sum becomes 62. The two numbers are
(1) 19, 7  
(2) 13, 7
(3) 7, 13  
(4)17, 3


7. How much will be the compound interest to be paid on a principal amount of Rs 85,000/- after 3 years at the rate of 6 p.c.p.a?
(1) Rs 16623.36/- 
(2) Rs 16236.36/-
(3) Rs 16326.36/- 
(4) Rs 16632.36/-


8. Yesterday Mansi typed an essay of 5000 words at the speed of 60 words per minute. Today she typed the same essay faster and her speed was 15% more than yesterday. What is the approximate difference in the time she took to type yesterday and the time she took to type today?
(1) 20 minutes 
(2) 30 minutes
(3) 10 minutes 
(4) 40 minutes


9. To Finish a work, B will take three times as long as A and C together and C will take twice as long as A and B together. If the three persons A, B and C together can finish the work in 20 days , then how long will A take to finish the work alone?
(1) 30 days  
(2) 45 days
(3) 48 days   
(4) 60 days


10. A square park is surrounded from outside by a path of 5 meters width. If the area of the path is 1700sq meters, then what is the area of the park?
(1) 3600sq m 
(2) 4900sq m
(3) 5625sq m 
(4) 6400sq m


11. In how many different ways can the letters of word ‘PREVIOUS’ be arranged in such a way that the vowels always come together?
(1) 50400  
(2) 4840
(3) 3260  
(4) 2880

12. A person drove a certain distance by car the speed of 35 km/h and returned on cycle at the speed of 10 km/h, If the whole journey took 18 hours. Then what distance did he drive on car?
(1) 80 km  
(2) 120 km
(3) 140 km  
(4) 150 km

13. A builder decided to build a house in 50 days. He employed 150 men at the beginning and another 80 men after 20 days and completed the work in the stipulated time. If he had not employed the additional men, how many days behind schedule would it have been finished?
(1) 10 days  
(2) 12 days
(3) 15 days  
(4) 16 days

14. A dealer bought an item at 10% discount on its original price. He sold it at 35% more than the original price. What percentage profit did he get?
(1) 25%  
(2) 45%
(3) 22.5%  
(4) 50%

15. Price register an increase of 10% on food grains and 15% on other items of expenditure. If the ratio of expenditure of an employee on food grains and other items be 2:5, by how much should his salary be increased in order that he may maintain the same level of consumption as before? Assume that there is no saving our of his monthly salary of Rs 2590.
(1) 13.57%  
(2) 12%
(3) 13%  
(4) 18.42%

ANSWERS
1. (2)
Total students are 40 × 15 = 600
So, 18 x 16 + (12 + 14) = 456
Left student is 10 and their average is =600-456= 144÷ 10=14.4

2. (1)
The interest in 2 years is 594.5 which is 10.25% of 5800. Hence the rate of interest is 5% p.a.

3. (2)
Upstream speed = 5 km/hr
Downstream speed = 15 km/hr
Speed of boat in still water = (5 + 15)/2 = 10 km/hr
Required time = 90/10 = 9 hrs

4. (5)
Let the rate of interest is=x
(X * 5000 * 2)/100 + (3000 * 4 * x)/100 = 2200
x = 10%

5. (4)
Let Car A takes t hrs to reach  the place
Distance is same,
35 t = 55(t – 7/2)
T = 77/8
Distance = 35 * 77/8 = 336.87 km

6. (3)
Let the number  be X and Y
Then 6y – x = 71 and 7x + y = 62
 Solving the equation
X = 7,  y = 13

7. (2) C.I. = 85000 × (19.1016/100)
= Rs 16236.36 Approx.

8. (3) Difference of time = 5000/60 − 5000/(60 * 1.15)
= 5000/60 − 5000/69
= 83.33 – 72.46
= 10 min (Approx.)

9. (3)
3*B’s daily work= (A+C)’s daily work
4*B’s daily work = (A+B+C)’s daily work = 1/20 
B’s daily work = 1/80 
2*C’s daily work = (A+B)’s daily work
3*C’s daily work = (A+B+C)’s daily work = 1/20
C’s daily work= 1/60
A’s daily work= 1/20 - (1/80 + 1/60) = 1/48
A can finish the work in 48 days.


10. (4)
Let the side of park be=’x’
Area of path= 2{(x + 10)5 + 5x}

  
1700=2(10x+50)
x = (850 - 50)/10 = 80m 
Area =(80)^2=6400 sq.m

11. (4)
Total letters are ‘8’ and No of vowels = 4
So total no of ways=5! * 4! = 2880

12. (3) Let the distance be x km
Time taken by car = x/35 and time taken on cycle = x/10
x/10 + x/35 = 18
 
13. (4) ,Let 150 men complete the work in x days , work done by 150 men in 20 days +work done by 230 men in 30 days=1
20/x + (230 * 30)/150x = 1
x = 66 days 
So it is 66-50 = 16 days behind the schedule

14. (4)
Let the original price to be Rs 100.
So he bought it at 10% discount ie Rs 90 and sells it at 35% more than the original rate ie Rs 135.
Actual profit is 135-90=Rs 45
So % profit = 45/90 * 100 = 50%

15.(1)
By the method of allegation:

Or, (15  - x)/(x - 10) = 2/5
Or, 75- 5x=2x-20
Or, 7x=95
Or, x=13.57%

 

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Quant Quiz

1.A sum of Rs 731 is distributed among A, B and C, such that A receives 25% more than B and B receives 25% less than C. What is C’s share in the amount?
(1)Rs 172       
(2)Rs 200       
(3)Rs262
(4)Rs 272       

2.Manoj sold an article for Rs 15000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price?
(1)Rs12,500       
(2)Rs13,500       
(3)Rs12,250
(4)Rs13,250       

3.What will be the compound interest accrued on an amount of Rs 10,000 @20p.c.p.a. in two years if the interest is compounded half-yearly?
(1)Rs4,400       
(2)Rs4,600       
(3)Rs4,641
(4)Rs 4,680       

4.A committee of 3 members is to be selected out of 3 men and 2 women. What is the probability that the committee has at least 1 woman?
(1)1⁄10            
(2)9⁄20    
(3)9⁄10
(4)1⁄20            

5.B and C together can complete a piece of work in 8 days. A and B can complete the same work in 12 days and A and C can complete the same work in 16 days. In how many days can A, B and C together can complete the work?
(1)3 3⁄9            
(2)7 5⁄13        
(3)7 5⁄12
(4)3 5⁄12        

6.The average speed of a car is 1 4⁄5 times the average speed of the bus. A tractor covers 575km in 23 hours. How much distance the car cover in 4 hours of the speed of the bus is twice the speed of the tractor?
(1)340km       
(2)480km   
(3)360km
(4)450 km       

7.A pump can fill a tank with water in 2 hours. Because of the leak, it took 2 1⁄3 hours to fill the tank. The leak can drain all the water of the tank in:
(1)4 1⁄3 hours       
(2)7hours       
(3)8 hours
(4)14 hours       

8.A shopkeeper mixed two verities of rice at Rs. 20/kg and Rs. 30/kg in the ratio 2 : 3 and sell the mixture at 10% profit. Find the price per kg at which he sold the mixture?
(1)Rs.26       
(2)Rs.28.8       
(3)Rs.28
(4)Rs.28.6       

9.The ratio of the present ages of Anju and Sandhya is 13:17 respectively. Four years ago the ratio of their respective ages was 11:15. What will be the respective ratio of their ages six years hence?
(1)3:4           
(2)7:8           
(3)4:5
(4)6:5           

10.A shopkeeper bought 30kg of wheat at the rate of Rs45 per kg. He sold 40% of the total quantity at the rate of Rs50 per kg. Approximately, at what price per kg should he sell the remaining quantity to make a profit of 25% overall?
(1)Rs54       
(2)Rs52       
(3)Rs60 
(4)Rs56   

Answers With Explanations:

1. (4)
Let C's share be Rs x.
Then, B gets =0.75 x.
A gets = 1.25×0.75x
x+0.75x+0.9375x=731
2.6875x=731
x=731⁄2.6875 =272

2. (1)
SP=Rs15000
SP after 10% discount= 15000-10%of15000= 15000-1500=Rs13500
Profit on SP= 8%
CP= 13500⁄108 ×100=Rs 12500

3. (3)
CI=10000[{(11⁄10 )×(11⁄10 )×(11⁄10 )×(11⁄10 )}-1]
4.(3)
Probability that the committee has at least one woman
= 1-P(no. of woman in the committee)
= 1-P(all men in the committee)
=1-1⁄10 =9⁄10 

5. (2)
(B+C)'s 1 day work= 1⁄8  ...(i)
(A+B)'s 1 day's work= 1⁄12  ...(ii)
(A+C)'s 1 day's work = 1⁄16  ...(iii)
On adding all these three equations,
2(A+B+C)'s one day's work = 1⁄8 +1⁄12 1⁄16 =(6+4+3)⁄48 =13⁄48
(A+B+C)'s one day's work= 13⁄96
∴A, B and C can complete the work in 96⁄13 =7 5⁄13 

6. (3)
Speed of the tractor= distance/ time
=575⁄23 =25kmph
∴speed of bus= 50kmph
∴speed of car= 9⁄5 ×50=90kmph
∴distance covered by the car in 4 hours= 4×90=360km

7. (4)
Work done by the leak in 1 hour = (1⁄2 -3⁄7 )=1⁄14
∴leak will empty the tank in 14 hours.

8. (4)
CP of mixture = (20*2+30*3)⁄2+3 =26
SP of the mixture = 1.1×26=28.6

9.(3)
Let the present ages of Anju and Sandhya be 13x and 17x years respectively.
∴13x-4⁄17x-4 =11⁄15
=>187x-44=195x-60
=>195x-187x=60-40
=>x=2
∴Required ratio= (13×2+6):(17×2+6)
=4:5

10.(3)
CP of wheat= 30×45=Rs1350
40% of 30kg =12kg
SP of 12kg = 12×50 = Rs 600
For 25% profit, total SP of all the wheat is 1350×125⁄100 =Rs 1687.5
Remaining wheat (30-12)= 8kg
Rate of remaining wheat = 1087.5⁄18 ≈Rs60

Give your answer in the comment section along with your timing and judge where you stand in the competition. 

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Formulae and Questions of Percentage

1.    Concept of percentage or Percentage formula

To express x% as a fraction: We have, x% x/100 Thus, 30%=30/100= 3/10

In simple terms we can conclude that percentage symbol "%" means 1/100

In case we are having a fraction and we have to calculate its percentage then we will multiply it      by 100.

that is, 

a/b=(a/b)×100)%

2.    Increase or decrease in percentage with price 
(1) If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure will be = [R/ (100+R)×100]%

( 2) If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure will be = [R/(100−R)×100]

3.    Results on population
Formula's on result of population are very important when we have to calculate the population n years after or n years before,
Let the population of a town be P now and suppose it increases at the rate of R% per annum, then
(1) Population after n years =P(1+R/100)ⁿ

(2)  Population before n years =P/(1+R/100)ⁿ

4.    Results on Depreciation
We know that value of a machine depreciate with time, so it will decrease with the time. To calculate the value of machine after n years or before n years, we use these formula's

Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. (1) Population after n years   = P(1−R/100)ⁿ

(2) Population before n years =P/(1−R/100)ⁿ

5.    Important results for Percentage
The formulas we are going to mention below is same as of increase or decrease in consumption with increase or decrease in the commodity price, just here we are in a bit different context.
(1) If A is R% more than B, then B is less than A by = [R/(100+R)×100]%

(2) If A is R% less than B, then B is more than A by = [R/(100−R)×100]%

Some Questions:- 

1.    Two numbers are less than third number by 30% and 37% respectively. How much percent is the second number less than by the first
(1) 20%
(2) 30 %
(3) 10%
(4) 40%

2.    In an examination, 34% of the students failed in mathematics and 42% failed in English. If 20% of the students failed in both the subjects, then find the percentage of students who passed in both the subjects.

(1) 40%                 (2) 41%

(3) 43%                 (4) 44%

3.    In the new budget , the price of kerosene oil rose by 25%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase ?

(1) 20%                 (2) 30%

(3) 22%                 (4) 24%

4.    The value of a machine depreciates at the rate of 10% per annum. If its present is Rs.1,62,000.? What was the value of the machine 2 years ago ?

(1) 200000             (2) 20000

(3) 2000                 (4) None of these

5.    A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?

(1) 60%                 (2) 62%

(3) 64%                 (4) 65%

 ANSWERS WITH EXPLANATIONS:

1.    (3) : Let the third number is x.
then first number = (100-30)% of x
= 70% of x = 7x/10

Second number is (63x/100)
Difference = 7x/10 - 63x/100 = 7x/10
So required percentage is, difference is what percent of first number
=> (7x/100 * 10/7x * 100 )% = 10%

2.    (4) : Failed in mathematics, n(A) = 34Failed in English, n(B) = 42

n(AUB) = n(A) + n (B) – n (A∩ B )

= 34 + 42- 20 = 56
Failed in either or both subjects are 56

Percentage passed = (100−56)%=44%

3.    (1) : Reduction in consumption = [((R/(100+R))*100]%? [(25/125)*100]%=20%.

4.    (1): Value of the machine 2 years ago
= Rs.[162000/(1-(10/100)²)]=Rs.[162000*(10/9)*(10/9)]= Rs.200000

5.    (3) : Let the number be x

Then, error =  (5/3)x – (3/5)x =(16/15)x

Error% = [(16x/15) /(5x/3)] * 100% = 64%

Give your answer in the comment section along with your timing and judge where you stand in the competition. 

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