Q1. Excluding Stoppages, The Speed Of A Bus Is 54 Kmph And Including Stoppages, It Is 45 Kmph. For How Many Minutes Does The Bus Stop Per Hour?

Speed of the bus excluding stoppages = 54 kmph.

Speed of the bus including stoppages = 45 kmph.

Loss in speed when including stoppages = 54 - 45 = 9kmph.

=> In 1 hour, bus covers 9 km less due to stoppages

Hence, time that the bus stop per hour = time taken to cover 9 km.

=distance / speed= 9 / 54 hour = 1/6 hour = 60/6 min=10 min.

Q2. A Can Lay Railway Track Between Two Given Stations In 16 Days And B Can Do The Same Job In 12 Days. With Help Of C, They Did The Job In 4 Days Only. Then, C Alone Can Do The Job In?

Work done by A in 1 day = 1/16

Work done by B in 1 day = 1/12

Let C takes x days to lay railway track between two given stations.

So work done by C in 1 day = 1/x

A, B and C together take 4 days to lay the railway track.

So, in 1 day they complete 14 of the total work together

So, 1/16 + 1/12 + 1/x = 1/4

=> 1/x = 1/4 - 1/16 - 1/12

=> 1/x = 5/48

=> x = 48/5.

Q3. A Alone Can Do A Piece Of Work In 6 Days And B Alone In 8 Days. A And B Undertook To Do It For Rs. 32

A completes the work in 6 days.

So, Work done by A in 1 day = 1/6.

=> A's 3-day work = 3/6 = 1/2.

B completes the work in 8 days

So, Work done by B in 1 day = 1/8

=> B's 3-day work = 3/8

The remaining work is done by C.

So the part of work done by C = 1 - (1/2+ 3/8) = 1/8.

So, C's share is 18 of 3200 = 3200 * 1/8 = 400.

Q4. N Number Of Persons Decided To Raise Rs.3 Lakhs By Equal Contribution From Each. Had They Contributed Rs.50 Each Extra, The Contribution Would Have Been Rs.3.25 Lakhs? How Many Persons Are There?

N X 50 = (325000 - 300000) = 25000

N = 25000 / 50

= 500.

Q5. A Man Takes 5 Hours 45 Min In Walking To A Certain Place And Riding Back. He Would Have Gained 2 Hours By Riding Both Ways. The Time He Would Take To Walk Both Ways Is?

Given that time taken for riding both ways will be 2 hours lesser than the time needed for waking one way and riding back.

From this, we can understand that time needed for riding one way = time needed for waking one way - 2 hours.

Given that time taken in walking one way and riding back = 5 hours 45 min

Hence the time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min.

Q6. A Money Lender Finds That Dues To A Fall In The Annual Rate Of Interest From 8% To 7x3/4%, His Yearly Income Diminishes By Rs.61.5

Let the capital be Rs. x.

Then, = (x × 8×1/100) - (x × 31/4×1/100)

= 61.50.

‹=›32x - 31x =6150×4

‹=›x= 24600.

Q7. A Woodentoy Is Bought For Rs. 56000 And Sold At Profit Of 25 %. Find Its Selling Price?

Cost price = Rs. 56000

Profit % = 25 %

Selling price = [(100 + Gain %)/100] * Cost price

Selling price = (125 /100) x 56000

Selling price = 70,000.

Q8. The H.c.f Of Two Numbers Is 11 And Their L.c.m Is 77

Other number = (11×7700 / 275)

= 308.

Q9. How Many 4 Letters Words With Or Without Meaning, Can Be Formed Out Of The Letters Of The Word, 'logarithms', If Repetition Of Letters Is Not Allowed?

'LOGARITHMS' contains 10 different letters.

Required number of words = Number of arrangements of 10 letters, taking 4 at a time.

‹=› 10_{p4}

‹=› (10 x 9 x 8 x 7)

‹=› 5040.

Q10. In An Examination, 35% Of The Students Passed And 455 Failed. How Many Students Appeared For The Examination?

Let the number of students appeared be x.

Then, 65% of x = 455

‹=›65 / 100 x = 455

‹=› x= [455 x 100 / 65]

= 700.

Q11. If The Sum And The Difference Of Two Numbers Are 20 And 8 Respectively, Then The Difference Of Their Square Is?

Let the numbers be x and y.

Then, x + y = 20 and x - y = 8.

Therefore, x2 - y2 = (x + y)(x - y)

‹=› 20 x 8

‹=› 160.

Q12. When A Plot Is Sold For Rs. 18,700, The Owner Loses 15%. At What Price Must That Plot Be Sold In Order To Gain 15%?

Let the C.P. of the plot = Rs. x.

Given that x - 15% of x = 18700.

=> (85/100) * x = 18700.

=> x = 22000.

So the cost price (C.P.) of the plot = Rs. 22000.

S.P. of plot for 15% profit = 22000 + 15% of 22000 = 22000*(115/100) = 25300.

Q13. If Selling Price Is Doubled, The Profit Triples. Find The Profit Percent?

Let the C.P. be x and the S.P. be y

So the profit is (y - x) ---------------------------- (1)

Now, the S.P. is doubled. So the new S.P. = 2y

The new profit = (2y - x)

Given that when S.P. is doubled, profit increases 3 times

=> New profit = 3 * old profit

=> (2y - x) = 3(y - x)

=> y = 2x

So, the profit = (y - x) = (2x - x) = x

% profit = (x / x) * 100 % = 100%.

Q14. The Sum Of Two Numbers Is 2

Let the numbers be x and (22 - x).

Then, 5x = 6(22 - x)

‹=› 11 x = 132

x = 12.

So, the numbers are 12 and 10.

Q15. A Cube Of Edge 5 Cm Is Cut Into Cubes Of Each Edge 1 Cm. The Ratio Of The Total Surface Area Of One Of The Small Cubes To That Of The Large Cube Is Equal To?

Required ratio = (6x1x1 / 6x5x5)

‹=›1/ 25

‹=›1: 125.

Q16. A Train 100 M Long Is Running At The Speed Of 30 Km/hr. Find The Time Taken By It To Pass A Man Standing Near The Railway Line?

Speed of the train = (30 x 5/18) m/sec

= (25 / 3) m/sec.

Distance moved in passing the standing man = 100 m.

Required time taken = 100 / (25 / 3)

= (100 x 3 / 25) sec

= 12 sec.

Q17. The Cost Of Painting The Whole Surface Area Of A Cube At The Rate Of 13 Paise Per Sq.cm Is Rs. 343.9

Surface area = (34398 / 13)

‹=›2646cm3

‹=›6a2= 2646

‹=›a2= 441

‹=›a = 21.

So, volume = (21x21x21) cm3= 9261cm3.

Q18. A Pump Can Fill A Tank With Water In 2 Hours. Because Of A Leak, It Took 2x1/3 Hours To Fill The Tank. The Leak Can Drain All The Water Of The Tank In?

Work done by the leak in 1 hour = (1/2 - 3/7)

‹=›1/14.

Leak will empty the tank in 14 hours.

Q19. 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 Seconds. The Speed Of The Train Is?

Let the speed of the train be x km/hr.

Given, Speed of the man = 5 km/hr.

Since both the train and man are moving in the same direction so the speed of the train (relative to man) would be (x-5) km/hr.

Length of the train = 125 m = 125/1000 km = 18 km

Time taken to cross the man = 10 sec = 10/3600 hrs. = 1/360 hrs.

So speed =distance/time.

=> x-5 =360/ 8.

=> 8x - 40 = 360.

=> 8x = 400.

=> x = 50 km/hr.

Q20. If A Number X Is 10% Less Than Another Number Y And Y Is 10% More Than 125, Then X Is Equal To?

y = 125 + 10% of 125

= 125 + 12.50

= 137.50.

x = 137.50 - 10% of 137.50

= 137.50 - 13.75

= 123.75.

Q21. The Largest Four Digit Number Which Is A Perfect Cube, Is?

Clearly, 9261 is a perfect cube satisfying the given property.

Q22. The Cube Root Of .000216 Is?

(.000216)^{1/3} = (216 / 10^{6})^{1/3}

= (6 x 6 x / 10^{2} x 10^{2} x 10^{2})^{1/3}

= 6 / 10^{2}

= 6 / 100

= .06

Q23. Two Trains Start From A And B Respectively And Travel Towards Each Other At A Speed Of 60 Km/hr. And 75 Km/hr. Respectively. By The Time They Meet, The Second Train Has Traveled 70 Km More Than The Fi

At the time of meeting, let the distance traveled by the first train be x km.

Then, distance covered by the second train is (x + 70) km.

=> x/60 = (x + 70)/75.

=> 75x = 60x + 60*70.

=> 15x = 4200 = x = 280 km.

So, distance between A and B = (x + x + 70)

= 280 + 280 + 70

= 630 km.

Q24. A Is Thrice As Good As Workman As B And Therefore Is Able To Finish A Job In 60 Days Less Than B. Working Together, They Can Do It In?

Let B takes x days to complete the job.

Since A is 3 times better than B, A takes one third of the time taken by B.

So, A can finish the job in x/3 days.

Given that time taken by A to complete the work is 60 days less than that of B

So, x/3 = x - 60.

=> x = 90.

So, B does the job in 90 days and A does in (90-60) days = 30 days.

Fraction of job done by A in 1 day = 1/30 and fraction of job done by B in 1 day = 1/90.

When working together, work done by A and B in 1 day = 1/30 + 1/90 = 2/45.

So, total time taken by A and B to complete the work together = 45/2.

Q25. A Classroom Has Equal Number Of Boys And Girls. Eight Girls Left To Play Kho-kho, Leaving Twice As Many Boys As Girls In The Classroom. What Was The Total Number Of Girls And Boys Present Initially?

Let the number of boys = x.

Then, number of girls = x.

Now, 2(x - 8) = x.

x = 16.

Total number of students = 2x = 2 x16 = 32.

Q26. 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 Per Annum

Let the rate be R% p.a.

Then, (5000xRx2/100) + (3000xRx4/100)

‹=›100R+120R= 2200

‹=›R= (2200/220)

Rate ‹=›10%.

Q27. In A Lottery, There Are 10 Prizes And 25 Blanks. A Lottery Is Drawn At Random. What Is The Probability Of Getting A Prize?

P (getting a prize) = 10 / (10+25)

‹=› 10 / 35

‹=› 2 / 7.

Q28. The Cost Price Of 20 Articles Is The Same As The Selling Price Of X Articles. If The Profit Is 25%, Then The Value Of X Is?

Let the cost price of 1 article be z.

So, the cost price of 20 article = 20z ------------------------- (1)

Selling Price of 20 articles = 20z + 25% of 20z = 25z

=> Selling Price of 1 article = 25z/20 = (5/4) *z

=> Selling Price of x articles = (5/4) *z*x ------------------------- (2)

Given that Selling Price (S.P.) of x articles = Cost Price (C.P.) of 20 articles

=> (5/4) *z*x = 20z

=> x = 16.

Q29. The Smallest Number Which When Diminished By 7, Is Divisible By 12, 16, 18, 21 And 28 Is?

Required numbers = (L.C.M of 12, 16, 18, 21, 28) + 7

‹=›1008 + 7

= 1015.

Q30. Pipe A Can Fill A Tank In 5 Hours, Pipe B In 10 Hours And Pipe C In 30 Hours. If All The Pipes Are Open, In How Many Hours Will The Tank Be Filled?

Part filled by (A+B+C) in 1 hour = (1/5 + 1/6 + 1/30)

‹=› 1/3.

All the three pipes together will fill the tank in 3 hours.

Q31. A Man Sitting In A Train Which Is Travelling At 50 Kmph Observes That A Goods Train, Travelling In Opposite Direction, Takes 9 Seconds To Pass Him. If The Goods Train Is 280 M Long, Find Its Speed?

Relative Speed = (280 / 9) m/sec

= (280/9 x 18/5)

= 112 kmph.

Speed of the train = (112 - 50) kmph

= 62 kmph.

Q32. Two Trains Running In Opposite Directions Cross A Man Standing On The Platform In 27 Seconds And 17 Seconds Respectively And They Cross Each Other In 23 Seconds. The Ratio Of Their Speeds Is?

Let the speeds of the two trains be a m/sec and b m/sec respectively.

Then, length of the first train = 27a meters,

and length of the second train = 17b meters.

so time = distance/ speed.

=> 23 = (27a+17b) / (a+b).

=> 23a + 23b = 27a +17b

=> 23a - 27a = 17b - 23b

=> -4 a = -6 b

=> 2 a = 3 b

=> a/ b= 3/2.