Most Important Quant Questions Based On CGLE Tier I 2017

Hello Students, SSC CGL 2017 Exam has started with a bang and complete surprise in a few sections. It's important to understand the exam pattern and types of questions are asked in CGL tier-1 2017. Hence, we are providing some important questions which will give you better idea about Quant section. Read these 25 Questions and be better prepared. we will keep providing such questions for all subjects. Keep studying with Adda247. we wish you all the best for the exam.

Q1. The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is:
(a)625
(b)630
(c)640
(d)650

Q2. Five years ago the average age of husband and wife was 23 years. Today the average age of husband, wife, and child is 21 Yrs. How old is the child?
(a) 3 Yrs
(b) 7 Yrs
(c) 12 Yrs
(d) 2 Yrs

Q3. The Government reduced the price of sugar by 10 percent. By this a consumer can buy 6.2 kg more sugar for Rs. 837. The reduced price per kg of sugar is
(a) Rs. 12.50
(b) Rs. 13.00
(c) Rs. 13.50
(d) Rs. 14.00

Q4. Apples are purchased @ 10 apples/Re. How many apples should be sold for one Rupee to obtain a profit of 25%?
(a) 6
(b) 8
(c) 12
(d) 4

Q5. Sham sells some articles to Chanda at a profit of 20%. Chanda now sells this article to Mayank at a loss of 30% and Mayank sells this articles at a profit of 20%. If CP of Chanda is Rs. 150, then what is the SP of Mayank?
(a) Rs. 105
(b) Rs. 87.5
(c) Rs. 125
(d) Rs. 126

Q12. A thief steals a car at 1.30 p.m. and drives it off at 40 km/hr. The theft is discovered at 2 p.m. and the owner sets off in another car at 50 km/hr. He will overtake the thief at
(a) 5 p.m.
(b) 4 p.m.
(c) 4.30 p.m.
(d) 6 p.m.

Q13. If the total income of the family is Rs. 25,000, then the amount spent on Rent and Food together is
(a) Rs. 17,250
(b) Rs. 14,750
(c) Rs. 11,250
(d) Rs. 8,500

S13. Ans.(b)
Sol. 100% → 25,000
Rent + Food → (14 + 45)% = 59%
1% → 250

Q14. What is the ratio of the expenses on Education to the expenses on Food?
(a) 1: 3
(b) 3: 1
(c) 3: 5
(d) 5: 3

S14. Ans.(a)
Sol. Ratio of expenses
Education: Food → 15: 45
= 1: 3

Q15. Expenditure on Rent is what percent of expenditure of Fuel?
(a) 135%
(b) 156%
(c) 167%
(d) 172%

S15. Ans.(b)
Sol. Expenditure on Rent = 14%
Expenditure on Fuel → 9%
Required Ratio = × 100
= 155.54
≈ 156%

Q16. Which three expenditures together have a central angle of 108°?
(a) Fuel, Clothing and Others
(b) Fuel, Education and Others
(c) Clothing, Rent and Others
(d) Education, Rent and Others

S16. Ans.(b)
Sol. 100% have a central angle of 360°
108° → 30%
Check from option (b)

Q21.The parallel sides of a trapezium are 25 cm and 13 cm; its nonparallel sides are equal, each being 10 cm. Find the area of the trapezium.
(a) 154 cm²
(b) 155 cm²
(c) 156 cm²
(d) 152 cm²

Q22. In a mixture of milk and water of volume 30 litres, the ratio of milk and water is 7: 3. Find the quantity of water to be added to the mixture to make the ratio of milk and water 1: 2.
(a) 30
(b) 32
(c) 33
(d) 35

Q23. A trader buys goods at 20% discount on marked price. If he wants to make a profit of 25% after allowing a discount of 20%, by what percent should his marked price be greater than the original marked price?
(a) 15%
(b) 65%
(c) 25%
(d) 20%

 

Q24. A passenger train 150 m long is travelling with a speed of 36 km/hr. If a man is cycling in the direction of train at 9 km/hr., the time taken by the train to pass the man is
(a) 10sec
(b) 15sec
(c) 18sec
(d) 20sec

 

Q25. The profit obtained by selling a book for Rs. 60 is the same as the loss obtained by selling this book for Rs. 42. What is the cost price of the book?
(a) Rs. 40
(b) Rs. 50
(c) Rs. 51
(d) None of these

 

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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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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) Rs 262                                  (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 selling 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) Rs 4,400                               (2) Rs 4,600               

(3) Rs 4,641                               (4) Rs 4,680  

4.    The average weight of 4 men is increased by 3kg when one of them who weighs 120 kg is replaced by another man. What is the weight of the new man?

     (1) 125 kg                                   (2) 150 kg

     (3) 122 kg                                   (4) 132 kg

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) 3³⁄₉                                        (2) 7⁵⁄₁₃                      

(3) 7⁵⁄₁₂                                      (4) 3⁵⁄₁₂ 

         

6.    The average speed of a car is 1⁴⁄₅ times the average speed of the bus. A tractor covers 575 km 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) 340 km                                 (2) 480 km     

     (3) 360 km                                 (4) 450 km     

7.    A pump can fill a tank with water in 2 hours. Because of the leak, it took 2¹⁄₃ hours to fill the tank. The leak can drain all the water of the tank in:
(1) 4¹⁄₃ hours                              (2) 7 hours                  

(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) 5:4                                         (4) 4:5 

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) Rs 54                                    (2) Rs 52                    

(3) Rs 50                                    (4) Rs 60   

Answers with Explanation:

            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.  (4)

            If the average is increased by 3 kg, then sum of weights 

            increases  by 3 x 4 = 12 kg .

            And this increase in weight is due to the extra weight included 

            due to the inclusion of  new person.

            Weight of new man = 120 + 12 = 132 kg.

            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.(4)

            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.       (4)

            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) = 18kg

             Rate of remaining wheat = ^1087.5⁄₁₈ ≈Rs60                  

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Details of Triangle and its Properties - Part - II

As we all know, a triangle is a shape that consists of three sides and three angles. Taking a look at the triangle's angles often helps us find out what kind of triangle we are dealing with.

Here are some facts to remember:

• The three angles in a triangle always add up to 180⁰
• The three angles of an equilateral triangle are all equal to 60⁰
• Two angles of an isosceles triangle are equal.
• One angle of a right-angled triangle is 90⁰
• All angles of an acute-angled triangle are acute angles, thus smaller than 90⁰
• One angle of an obtuse-angled triangle is obtuse, thus larger than 90⁰ and smaller than 180⁰

•  Click here for Basic Triangle Part - I

If two triangles are congruent they have equal sides, equal areas. 

Condition for congruence:

1. SAS condition

If two sides and the included angle of one triangle is equal to the corresponding sides and included angle of the other triangle, then both triangles are congruent.
AB = DE, BC = EF and ∠B = ∠E, then ΔABC≈ΔDEF

2. ASA condition

If two angles and the included side of one triangle is equal to the corresponding two angles and    the included side of the other triangle, then both triangles are congruent.

If ∠A = ∠D, ∠B = ∠E and AB = DE, then ΔABC≈ΔDEF

3. SSS condition

If three sides of one triangle is equal to the corresponding three sides of other triangle then both    triangles are congruent.

  If AB = DE, AC = DF and BC = EF, then ΔABC≈ΔDEF

4. RHS condition

If the two triangles are right-

angled triangle and hypotenuse and one side of one triangle is equal    to the hypotenuse and corresponding side of other triangle, then both triangles are congruent.

if ∠B =∠E = 90°, AC = DF and AB = DE or BC = EF, then ΔABC≈ΔDEF

Note:  

 i.   All the congruent triangles are similar but all similar triangles are not congruent.

 ii.  The ratio of the areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides.

The following four theorems are most important in solving questions on triangles.

Pythagoras’ theorem: In a right angle triangle the square of the hypotenuse is equal to the sum of the squares of other two sides.

Pythagorean triplet: There are certain triplets which satisfy the pythagoras’ theorem and are commonly, called pythagorean triplet.

 For example: 3, 4, 5;    5, 12, 13;    24, 10, 26;    24, 7, 25;    15, 8, 17

Appolonious theorem: 

In triangle ABC, AD is median, which divides BC into two equal parts. Then,

AB²+AC²=2(AD²+BD²)=2(AD²+DC²)

 Stewart theorem:

In Triangle ABC, AD divides side BC in the ratio m and n. (Here AD need not be median) then, 

m.b²+n.c²=a(d²+mn)

Mean proportionality and Mid Point theorem:

In the first triangle, DE // BC so AD/DB=AE/EC

In the second triangle, D and E are mid points of AB and AC respectively. Which implies, AD/DB=AE/EC=1

Also, DE=1/2BC

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