Q1. The Sum Of The Ages Of A Son And Father Is 56 Years After Four Years The Age Of The Father Will Be Three Times That Of The Son. Their Ages Respectively Are?

Present ages of son and father be x years (56 -x)years

(56- x +4) = 3(x + 4) or 4x =48 or x = 12

Ages are 12 years, 44 years.

Q2. Four Car Rental Agencies A, B, C And D Rented A Plot For Parking Their Cars During The Night. A Parked 15 Cars For 12 Days, B Parked 12 Cars For 20 Days, C Parked 18 Cars For 18 Days And D Parked 16 C

The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15

= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60

Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.

The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k

It is given that A paid Rs. 1125

45k = 1125 => k = 25

246k = 246(25) = Rs. 6150

Thus the total rent paid by all the four agencies is Rs. 6150.

Q3. The Price Of An Article Is Cut By 10%. To Restore It To The Former Value, The New Price Must Be Increased By?

Let the price of the article = Rs.100

New price = 100 – 10 = 90

Therefore the new price must be increased by(100−90)×100/90=100/9%=11 1/9%.

Q4. A Train 110 M Long Is Running With A Speed Of 60 Km/hr. In What Time Will It Pass A Man Who Is Running At 6 Km/hr In The Direction Opposite To That In Which The Train Is Going?

Speed of train relative to man = 60 + 6 = 66 km/hr.

= 66 * 5/18 = 55/3 m/sec.

Time taken to pass the men = 110 * 3/55 = 6 sec.

Q5. Pushpa Is Twice As Old As Rita Was Two Years Ago If The Difference Between Their Ages Is 2 Years, How Old Is Pushpa Today?

Rita’s age 2 years ago be x years

Pushpa’s present age =(2x) years

2x –(x +2) =2 => x =4

Therefore pushpa’s present age = 8 years.

Q6. A And B Invests Rs.10000 Each, A Investing For 8 Months And B Investing For All The 12 Months In The Year. If The Total Profit At The End Of The Year Is Rs.25000, Find Their Shares?

The ratio of their profits A:B = 8:12 = 2:3

Share of A in the total profit = 2/5 * 25000 = Rs.10000 Share of A in the total profit = 3/5 * 25000 = Rs.15000.

Q7. How Many Of The Following Numbers Are Divisible By 132?

264, 396, 462, 792, 968, 2178, 5184, 6336

132 = 11 * 3 * 4

Clearly, 968 is not divisible by 3

None of 462 and 2178 is divisible by 4

And, 5284 is not divisible by 11

Each one of the remaining four numbers is divisible by each one of 4, 3 and 11.

So, there are 4 such numbers.

Q8. A Started A Business With An Investment Of Rs. 70000 And After 6 Months B Joined Him Investing Rs. 1200

Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6

Total profit = Rs. 52000

Share of B = 6/13 (52000) = Rs. 24000.

Q9. 9 3/4 + 7 2/17 – 9 1/15 = ?

Given sum = 9 + 3/4 + 7 + 2/17 – (9 + 1/15)

= (9 + 7 – 9) + (3/4 + 2/17 – 1/15)

= 7 + (765 + 120 – 68)/1020 = 7 817/1020.

Q10. A, B And C Started A Business With Capitals Of Rs. 8000, Rs. 10000 And Rs. 12000 Respectively. At The End Of The Year, The Profit Share Of B Is Rs. 15

Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6

And also given that, profit share of B is Rs. 1500

=> 5 parts out of 15 parts is Rs. 1500

Now, required difference is 6 – 4 = 2 parts

Required difference = 2/5 (1500) = Rs. 600.

Q11. A And B Start A Business, With A Investing The Total Capital Of Rs.50000, On The Condition That B Pays A Interest

Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.

Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.

Let ‘P’ be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)

Total income of B = only his share from the remaining profit = ‘P’, as A and B share the remaining profit equally.

Income of A = Twice the income of B

(2500 + 18000 + P) = 2(P)

P = 20500

Total profit = 2P + 18000

= 2*20500 + 18000 = 59000.

Q12. The Wheels Revolve Round A Common Horizontal Axis. They Make 15, 20 And 48 Revolutions In A Minute Respectively. Starting With A Certain Point On The Circumference Down Wards. After What Interval Of T

Time for one revolution = 60/15 = 4

60/ 20 = 3

60/48 = 5/4

LCM of 4, 3, 5/4

LCM of Numerators/HCF of Denominators =

60/1 = 60.

Q13. If The Length, Breadth And The Height Of A Cuboid Are In The Ratio 6: 5: 4 And If The Total Surface Area Is 33300 Cm^{2}, Then Length Breadth And Height In Cms, Are Respectively?

Length = 6x

Breadth = 5x

Height = 4x in cm

Therefore, 2(6x × 5x + 5x × 4x + 6x × 4x) = 33300

148x^{2} = 33300

=> x^{2} = 33300/148 = 225

=> x = 15.

Therefore, Length = 90cm,

Breadth = 75cm,

Height = 60cm

90, 75 , 60 cm.

Q14. Two-fifth Of One-third Of Three-seventh Of A Number Is

Let the number be x. Then,

2/5 of 1/3 of 3/7 of

x = 15 => x = (15 * 5/3 * 3 * 5/2) = 525/2

40% of 525/2 = (40/100 * 525/2) = 105.

Q15. A Train Moves Fast A Telegraph Post And A Bridge 264 M Long In 8 Sec And 20 Sec Respectively. What Is The Speed Of The Train?

Let the length of the train be x m and its speed be y m/sec.

Then, x/y = 8 => x = 8y

(x + 264)/20 = y

y = 22

Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr.

Q16. If 35% Of A Number Is 12 Less Than 50% Of That Number, Then The Number Is?

Let the number be x. Then,

50% of x – 35% of x = 12

50/100 x – 35/100 x = 12

x = (12 * 100)/15 = 80.

Q17. A Drink Vendor Has 80 Liters Of Maaza, 144 Liters Of Pepsi And 368 Liters Of Sprite. He Wants To Pack Them In C, So That Each Can Contains The Same Number Of Liters Of A Drink, And Doesn’t Want To Mix

The number of liters in each can = HCF of 80, 144 and 368 = 16 liters.

Number of c of Maaza = 80/16 = 5

Number of c of Pepsi = 144/16 = 9

Number of c of Sprite = 368/16 = 23

The total number of c required = 5 + 9 + 23 = 37 c.

Q18. A And B Starts A Business With Rs.8000 Each, And After 4 Months, B Withdraws Half Of His Capital How Should They Share The Profits At The End Of The 18 Months?

A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000.

So, the investment of B for remaining 14 months is Rs.4000 only.

A : B

8000*18 : (8000*4) + (4000*14)

14400 : 88000

A:B = 18:11.

Q19. The Price Of An Article Has Been Reduced By 25 %. In Order To Restore The Original Price, The New Price Must Be Increased By?

Let original price = Rs. 100.

Reduced Price = Rs. 75.

Increase on Rs. 75 = Rs. 25

Increase on 100 = (25/75 x 100) % = 33 1/3 %.

Q20. Sameer Spends 40 % Of His Salary On Food Article, And 1/3 Rd Of The Remaining On Trport. If He Saves Rs. 450 Per Month Which Is Half Of The Balance After Spending On Food Items And Trport. What Is Thi

Suppose, salary = Rs. 100

Expenditure on food = Rs. 40

Balance = Rs. 60

Expenditure on trport = 1/3 × Rs. 60 = Rs. 20

Now, balance = Rs. 40

Saving = Rs. 20

If saving is = Rs. 20

Salary = Rs. 100

If saving is Rs. 450,

salary = Rs (100/20 x 450) = Rs. 2250.

Q21. The Sum Of The Ages Of 5 Children Born At The Intervals Of 3 Years Each Is 50 Years. What Is The Age Of The Youngest Child?

Let the ages of the children be x, (x + 3), (x + 6), (x + 9) and (x +12) years.

Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50

5x = 20 => x = 4.

Age of youngest child = x = 4 years.

Q22. A 300 M Long Train Crosses A Platform In 39 Sec While It Crosses A Signal Pole In 18 Sec. What Is The Length Of The Platform?

Speed = 300/18 = 50/3 m/sec.

Let the length of the platform be x meters.

Then, (x + 300)/39 = 50/3

3x + 900 = 1950 => x = 350 m.

Q23. Find The Lowest 4-digit Number Which When Divided By 3, 4 Or 5 Leaves A Remainder Of 2 In Each Case?

Lowest 4-digit number is 1000.

LCM of 3, 4 and 5 is 60.

Dividing 1000 by 60, we get the remainder 4@Thus, the lowest 4-digit number that exactly divisible by 3, 4 and 5 is 1000 + (60 – 40) = 1020.

Now, add the remainder 2 that’s required. Thus, the wer is 1022.

Q24. How Many Meters Of Carpet 63cm Will Be Required To Be A Floor Of A Room 14m By 9cm?

Width of the carpet = 63/100 m let it’s length be x metres

Then x × 63/100 = 14 x 9

=> x =(14 x 9 x 100/63) = 200m

Length = 200m.

Q25. The Length Of A Rectangular Increased By 10% And It;s Breadth Is Decreased By 10 %. Then The Area Of The New Rectangle Is?

Length of the be let ‘l’ units and breadth be b units

Area =lb sq. Units

Now length =(110/100 l) = 11l/10

New breadth =(90/100 b) = 96/10

Now area (11l/10 x 96/10)Sq.units = (99/100 lb)sq.unit

Area decreased = (lb -99/100 lb)sq.units =lb/100 sq.Units

Percentage decreased =(lb/100 x 1/lb x 100)% = 1%.

Q26. A Is A Working Partner And B Is A Sleeping Partner In The Business. A Puts In Rs.15000 And B Rs.25000, A Receives 10% Of The Profit For Managing The Business The Rest Being Divided In Proportion Of Th

15:25 => 3:5

9600*10/100 = 960

9600 – 960 = 8640

8640*3/8 = 3240 + 960

= 4200.

Q27. Rajan Got Married 8 Years Ago. His Present Age Is 6/5 Times His Age At The Time Of His Marriage. Rajan’s Sister Was 10 Years Younger To Him At The Time Of His Marriage. The Age Of Rajan’s Sister Is?

Let Rajan’s present age be x years.

Then, his age at the time of marriage = (x – 8) years.

x = 6/5 (x – 8)

5x = 6x – 48 => x = 48

Rajan’s sister’s age at the time of his marriage = (x – 8) – 10 = 30 years.

Rajan’s sister’s present age = (30 + 8) = 38 years.

Q28. The Income Of A Broker Remains Uncharged Though The Rate Of Commission Is Increased From 4 % To 5 % The Percentage Of A Slump In Business Is?

Let the business value changes from x to y.

Then 4 % of x = 5 % of y of 4/100 × x = 5/100 × y

or y = 4/5 x.

Change in business = (x – 4/5 x) = 4/5 x.

Percentage slump in business

= (1/5 x ×1/x × 100)% = 20%.

Q29. A Jogger Running At 9 Km/hr Along Side A Railway Track Is 240 M Ahead Of The Engine Of A 120 M Long Train Running At 45 Km/hr In The Same Direction. In How Much Time Will The Train Pass The Jogger?

Speed of train relative to jogger = 45 – 9 = 36 km/hr.

= 36 * 5/18 = 10 m/sec.

Distance to be covered = 240 + 120 = 360 m.

Time taken = 360/10 = 36 sec.

Q30. Which One Of The Following Numbers Is Exactly Divisible By 11?

(4 + 5 + 2) – (1 + 6 + 3) = 1, not divisible by 11.

(2 + 6 + 4) – (4 + 5 + 2) = 1, not divisible by 11.

(4 + 6 + 1) – (2 + 5 + 3) = 1, not divisible by 11.

(4 + 6 + 1) – (2 + 5 + 4) = 0.

So, 415624 is divisible by 11.

Q31. A Train Speeds Past A Pole In 15 Sec And A Platform 100 M Long In 25 Sec, Its Length Is?

Let the length of the train be x m and its speed be y m/sec.

Then, x/y = 15 => y = x/15

(x + 100)/25 = x/15 => x = 150 m.

Q32. The Difference Between A Number And Its Two-fifth Is 5

Let the number be x. Then,

x – 2/5 x = 510

x = (510 * 5)/3 = 850

10% of 850 = 85.

Q33. A Room Is 6 Meters 24 Centimeters In Length And 4 Meters 32 Centimeters In Width. Find The Least Number Of Square Tiles Of Equal Size Required To Cover The Entire Floor Of The Room?

Length = 6 m 24 cm = 624 cm

Width = 4 m 32 cm = 432 cm

HCF of 624 and 432 = 48

Number of square tiles required = (624 * 432)/(48 * 48) = 13 * 9 = 117.

Q34. 66% Of 33.33% Of 66.66% Of ? = 30

16.66% of 33.33% of 66.66% of x = 30

= 1/6 of 1/3 of 2/3 of x = 30

=> (30 * 6 * 3 * 3)/2 => x = 810

Q35. A Boat Goes 24 Km Downstream In 10 Hours, It Takes 2 Hours More To Cover The Same Distance Against The Stream. What Is The Speed Of The Boat In Still Water?

Speed downstream = 24/10 km/hr = 2.4 km/hr

Speed upstream = 24/12 km/hr = 2 km/hr

Speed of the boat in still water = ½ (2.4 +2)km/hr = 2.2 km/hr.

Q36. A Train Passes A Station Platform In 36 Sec And A Man Standing On The Platform In 20 Sec. If The Speed Of The Train Is 54 Km/hr. What Is The Length Of The Platform?

Speed = 54 * 5/18 = 15 m/sec.

Length of the train = 15 * 20 = 300 m.

Let the length of the platform be x m . Then,

(x + 300)/36 = 15 => x = 240 m.

Q37. The Surface Area Of A Cube Is 726m^{2}, Its Volume Is?

6a^{2}= 726

=> a^{2} = 121

=> a = 11 Cm

Therefore, Volume of the cube

= (11 × 11 × 11) cm^{3} = 1331 cm^{3}.

Q38. Find The Greatest Number That, While Dividing 47, 215 And 365, Gives The Same Remainder In Each Case?

**Calculate the differences, taking two numbers at a time as follows:**

(215-47) = 168

(365-215) = 150

(365-47) = 318

HCF of 168, 150 and 318 we get 6, which is the greatest number, which while dividing 47, 215 and 365 gives the same.

emainder in each cases is 5.

Q39. The Speed Of A Motor Boat Is That Of The Current Of Water As 36:

Let the speed of motor boat be 36x km/hr and that of current of water be 5x km/hr

Speed downstream = (36x +5x)km/hr = 41x km/hr

Speed upstream = (36 -5x)km/hr = 31x km/hr

Distance covered downstream = (41x × 31/6)km

Distance upstream = [1271x/6 × 1/31x]hrs

= 41/6 hrs = 6hrs 50 min.

Q40. The Length Of A Rectangle Is Increased By 60 %. By What Percent Would The Width Have To Be Decreased To Maintain The Same Area?

Let length = 100 m.

Breath = 100 m.

New length = 160 m.

New breath = x meters

Then, = 160 × x = 100 × 100

(or) X = (100 ×100)/160 × 125/2

Decrease in breadth = (100- 125/2) % = 37 ½ %.

Q41. If 20% Of A Number, Then 120% Of That Number Will Be?

Let the number x. Then,

20% of x = 120

x = (120 * 100)/20 = 600

120% of x = (120/100 * 600) = 720.

Q42. A Steamer Goes Downstream From One Port To Another In 4 Hours, It Covers The Same Distance Upstream In 5 Hours. If The Speed Of The Stream Is 2km/hr,the Distance Between The Two Parts Is?

Let the distance between the two parts be x km.

Then speed downstream = x/4 km/hr.

Speed Upstream = x/5 km/hr

Speed of the stream = ½ (x/4 –x/5)

Therefore, ½(x/4 –x/5) = @=> x/4 –x/5 = 4 => x = 80.

Hence, the distance between the two ports is 80km.

Q43. Water Tax Is Increased By 20% But Its Consumption Is Decreased By 20 %. Then, The Increase Or Decrease In The Expenditure Of The Money Is?

Let tax = Rs. 100 and consumption = 100 units

Original Expenditure = Rs. (100 × 100) = Rs. 10000

New Expenditure = Rs. (120 × 80) = Rs. 9600

Decrease in expenditure = (400/10000 x 100) % = 4 %.

Q44. How Many Seconds Will A 500 M Long Train Take To Cross A Man Walking With A Speed Of 3 Km/hr In The Direction Of The Moving Train If The Speed Of The Train Is 63 Km/hr?

Speed of train relative to man = 63 – 3 = 60 km/hr.

= 60 * 5/18 = 50/3 m/sec.

Time taken to pass the man = 500 * 3/50 = 30 sec.

Q45. A Train 125 M Long Passes A Man, Running At 5 Km/hr In The Same Direction In Which The Train Is Going, In 10 Sec. The Speed Of The Train Is?

Speed of the train relative to man = 125/10 = 25/2 m/sec.

= 25/2 * 18/5 = 45 km/hr

Let the speed of the train be x km/hr. Then, relative speed = (x – 5) km/hr.

x – 5 = 45 => x = 50 km/hr.

Q46. The Sum Of The Two Numbers Is 12 And Their Product Is 3

Let the numbers be a and b. Then,

a + b = 12 and ab = 35.

(a + b)/ab = 12/35

= (1/b + 1/a) = 12/35

Sum of reciprocals of given numbers = 12/35.

Q47. Ayesha’s Father Was 38 Years Of Age When She Was Born While Her Mother Was 36 Years Old When Her Brother Four Years Younger To Her Was Born. What Is The Difference Between The Ages Of Her Parents?

Mother’s age when Ayesha’s brother was born = 36 years.

Father’s age when Ayesha’s brother was born = (38 + 4) = 42 years.

Required difference = (42 – 36) = 6 years.

Q48. Two Trains 140 M And 160 M Long Run At The Speed Of 60 Km/hr And 40 Km/hr Respectively In Opposite Directions On Parallel Tracks. The Time Which They Take To Cross Each Other Is?

Relative speed = 60 + 40 = 100 km/hr.

= 100 * 5/18 = 250/9 m/sec.

Distance covered in crossing each other = 140 + 160 = 300 m.

Required time = 300 * 9/250 = 54/5 = 10.8 sec.

Q49. On Decreasing The Price Of T.v. Sets By 30 % Its Sale Is Increased By 20 %. What Is The Effect On The Revenue Received By The Shopkeeper?

Let price = Rs. 100, Sale = 100

Then Sale Value = Rs. (100 × 100) = Rs. 10000

New Sale Value = Rs. (70 × 120) = Rs. 8400

Decrease % = (1000/10000 x 100) % = 16 %.

Q50. P And Q Started A Business With Respective Investments Of Rs. 4 Lakhs And Rs. 10 Lakhs. As P Runs The Business, His Salary Is Rs. 5000 Per Month. If They Earned A Profit Of Rs. 2 Lakhs At The End Of T

Ratio of investments of P and Q is 2 : 5

Total salary claimed by P = 12 * 5000 = Rs. 60000

Total profit = Rs. 2 lakhs.

Profit is to be shared = Rs. 140000

Share of P = (2/7) * 140000 = Rs. 400000

Share of Q = Rs. 100000

Total earnings of P = (60000 + 40000) = Rs. 100000

Ratio of their earnings = 1 : 1.