## Deloitte Aptitude Placement Papers - Deloitte Aptitude Interview Questions and Answers

Q1. A Pump Can Be Operated Both For Filling A Tank And For Emptying It. The Capacity Of The Tank Is 2400 M

Let the filling potential of the pump = x m3/ min.

Then the emptying capacity of the pump = (x + 10) m3/ min.

Time required for filling the tank = 2400/x minutes

Time required for emptying the tank = 2400/x+10 minutes

Pump desires eight mins lesser to empty the tank than it wishes to fill it

⇒2400/x−2400/x+10=eight

⇒300/x−three hundred/x+10=1

⇒300/(x+10)−three hundred/x=x(x+10)

⇒3000=x2+10x

⇒x2+10x−3000=zero

(x+60)(x−50)=0

x = 50 or -60

Since x cannot be terrible, x=50

i.E.,filling ability of the pump = 50 m3/min.

Q2. A Race Course Is 400 M Long. A And B Run A Race And A Wins By 5m. B And C Run Over The Same Course And B Win By 4m. C And D Run Over It And D Wins By 16m. If A And D Run Over It, Then Who Would Win An

If A covers 400m, B covers 395 m

If B covers 400m, C covers 396 m

If D covers 400m, C covers 384 m

Now if B covers 395 m, then C will cover 396/four hundred×395=391.05m

If C covers 391.05 m, then D will cowl four hundred/384×391.05=407.24

If A and D run over 400 m, then D win with the aid of 7.2 m (approx.)

Q3. The Average Of Three Numbers Is seventy seven.The First Number Is Twice The Second And The Second Number Is Twice The Third. Find The First Number?

Here as in line with situation allow us to consider 0.33 variety = x,

then 2nd number = 2x and third wide variety = 4x,

Given that (4x+2x+x)/three = 77,

7x = three×seventy seven, x = 3 x eleven = 33,

first range = 4x = 4 x 33 = 132.

Q4. A Good Train And A Passenger Train Are Running On Parallel Tracks In The Same Direction. The Driver Of The Goods Train Observes That The Passenger Train Coming From Behind Overtakes And Crosses His Tr

Let the speeds of the two trains be s and 2s m/s respectively.

Also, assume that the lengths of the two trains are P and Q metres respectively.

Then,

P+Q/2s−s=60------(1)

and

P/2s−s=forty------(2)

On dividing these two equation we get:

P+Q/P=60/forty

P:Q = 2 : 1.

Q5. A Train Starts From Delhi At 6:00 Am And Reaches Ambala Cantt. At 10am. The Other Train Starts From Ambala Cantt. At 8am And Reached Delhi At eleven:30 Am, If The Distance Between Delhi And Ambala Cantt I

Average pace of educate leaving Delhi = 2004=50 km/hr

Average pace of educate leaving Ambala cantt. = 200×27=4007

By the time the alternative teach starts offevolved from Ambala cantt, the first teach had travelled 100 km

Therefore, the trains meet after:

=2 hundred−100/(50+400/7)=14/15hr

=14/15×60=56minutes

Hence they meet at eight:56 am.

Q6. Walking At The Rate Of 4 Kmph A Man Cover Certain Distance In 2 Hr 45 Min. Running At A Speed Of sixteen.5 Kmph The Man Will Cover The Same Distance In?

Distance = Speed × time

Here time = 2hr 45 min = 114 hr

Distance = 4×114=eleven km

New Speed =16.Five kmph

Therefore time = DS=1116.Five=forty min.

Q7. A Car Travels First Half Distance Between Two Places With A Speed Of40 Km/hr And Rest Of The Half Distance With A Speed Of 60 Km/hr.The Average Speed Of The Car Is?

Let the whole distance covered be S km.

Total time taken= S (2×40) + S (2×60) = 5S 240 hr

Average speed =S× 240 5S = 48 km/hr.

Q8. The Simplified Form Of Log(75/16) -2 Log(5/nine) +log(32/343) Is ?

Given Exp= log75/16 – 2 log5/nine + log32/343

= log [(25 x 3) / (4 x 4)] – log (25/81) + log [(16 x 2) / (81 x 3)]

= log(25 x three) – log ( 4 x 4 ) – log(25) + log81 + log(sixteen x 2) -log (81 x 3)

= log 25 + log 3 – log sixteen – log 25 + log eighty one + log sixteen + log 2 – log 81 – log 3

= log 2.

Q9. The Mean Daily Profit Made By A Shopkeeper In A Month Of 30 Days Was Rs. 35

Find the overall earnings made in the first 15 days:

Mean each day earnings for the first 15 days = Ra 275

Total earnings for the primary 15 days = 275 x 15 = Rs 4125.

Find the overall earnings for the closing 15 days:

10,500 - 4125 = Rs 6375.

Find the imply profit for the ultimate 15 days:

Mean profit = 6375 ÷ 15 = Rs 425.

Q10. Log Xy = one hundred And Log X2 = 10, Then The Value Of Y Is?

Log2x = 10 ⇒ x = 210.

∴ logx y = a hundred

⇒ y = x100

⇒ y = (210)one hundred [put value of x]

⇒ y = 21000.

Q11. A Man Sitting On A Train Travelling At The Rate Of 50 Km/hr Observes That It Takes 9 Sec For Goods Train Travelling In The Opposite Direction To Pass Him. If The Goods Train Is 187.5m Long. Find Its S

Let the speed of goods educate be x km/hr.

Then,

(50+x)×( 5 18 )= 187.5 9

⇒ x= 25 km/hr.

Q12. In A Kilometer Race, A Can Give B A 100 M Start And C A 150 M Start. How Many Meters Start Can B Give To C?

A can supply B a one hundred m begin and C a 150m.

Start me when A runs 1000m,

B runs 900m and C runs 850m.

When B runs 1000m,

C will run 1000 x (850/900) m (i.E. 8500/nine m) Thus,

B can give C a begin of - a thousand - (8500/nine), i.E. 500/9 m.

Q13. The Value Of Log2(1/sixty four) Is?

Log2(164)=xlog2(164)=x

Rewrite the equation as x=log2(164)x=log2(164).

X=log2(164)x=log2(164) Logarithm base 22 of 164164 is −6-6.

X=−6.

Q14. A Train Covers A Distance In 50 Min, If It Runs At A Speed Of 48 Kmph On An Average. The Speed At Which The Train Must Run To Reduce The Time Of Journey To 40 Min Will Be?

Time = 50/60=5/6 hr

Speed = 48 mph

Distance = S×T=48×five/6=forty km

Time = 40/60 hr

New speed = 40×3/2=60 kmph.

Q15. A Train Of Length 110 Meters Is Running At A Speed Of 60 Kmph.In What Time, It Will Pass A Man Who Is Running At 6 Kmph In Thedirection Opposite To That In Which The Train Is Going?

Distance = one hundred ten m

Relative speed = 60 + 6 = 66 kmph

(Since each the teach and the man are in transferring in contrary direction) = (66*5/18) m/sec = 55/3 m/sec.

Q16. The Ratio Between The Number Of Passengers Travelling By I And Ii Class Between The Two Railway Stations Is 1 : 50, Whereas The Ratio Of I And Ii Class Fares Between The Same Stations Is 3 :

Let x be the wide variety of passengers and y be the fare taken from passengers.

3xy + 50xy = 1325 => xy = 25

Amount collected from II magnificence passengers = 25 × 50 = Rs. 1250.

Q17. The Jogging Track In A Sports Complex Is 726 M In Circumference. Suresh And His Wife Start From The Same Point And Walk In Opposite Direction At 4.5 Km/hr And 3.Seventy five Km/hr Respectively. They Will Meet F

et both of them meet after T min

4500 m are protected by means of Suresh in 60 m.

In T min he will cowl 4500T60

Likewise, In T min Suresh's spouse will cowl 3750T60

Given,

4500T60+3750T60=726

T=five.28 mins.

Q18. A Passenger Train Takes Two Hours Less For A Journey Of 300 Km If Its Speed Is Increased By 5 Km/hr From Its Normal Speed. The Normal Speed Is?

Let the everyday speed be 's' km/hr

Then new velocity = (s+five) km/hr

three hundred/s−2=three hundred/s+5

On solving this equation we get:

s = 25 km/hr.

Q19. Which Greatest Possible Length Can Be Used To Measure Exactly 15 Meter 75 Cm, 11 Meter 25 Cm And 7 Meter 65 Cm?

We want to discover the HCF for given period.

15 meter 75 cm = 1575 cm.

Eleven meter 25 cm = 1125 cm 7 meter 65 cm = 765 cm.

1575 = 5 *five *three *three *7 1125 = five *five *5 *3 *3 765.

= 5 *3 *3 *17 HCF of 1575, 1125 and 765 is forty five (5 *3*three).

Q20. The Average Age Of All The Student Of A Class Is 18 Years. The Average Age Of Boys Of The Class Is 20 Years And That Of The Girls Is 15 Years. If The Number Of Girls In The Class Is 20, Then Find The

Let Boys in elegance = B

Girls in magnificence = 20

Now, (20B+15*20)/(B+20) = 18

⇒ B = 30.

Q21. There Were 35 Students In A Hostel. If The Number Of Students Increases By 7, The Expenses Of The Mess Increase By Rs. Forty two Per Day While The Average Expenditure Per Head Diminishes By Re

Let d be the common every day expenditure

Original expenditure = 35 × d

New expenditure = 35 × d + 42

New common expenditure might be :

(35 × d + forty two)/42 = d - 1

On fixing, we get d = 12

Therefore authentic expenditure = 35 × 12 = 420.

Q22. A Merchant Sold An Article At 10% Loss. If He Had Sold It Rs 450 More,8% Would Have Been Gained On The Cost Price. Find The Cost Price?

Let the cost charge be a hundred%. It is offered at 10% loss.

So it's miles bought at 90% of the value fee.

90 % of the cost charge + 450 = 108% of the Cost fee 18% of the fee rate = Rs 450 Cost fee of the e book = 450/18 x 100 = Rs 2500.

Q23. The Least Perfect Square, Which Is Divisible By Each Of 21, 36 And sixty six Is?

L.C.M. Of 21, 36, 66 = 2772 Now,

2772 = 2 x 2 x three x 3 x 7 x 11 To make it a great square,

it should be multiplied with the aid of 7 x @So,

required quantity = 2 x 2 x three x three x 7 x 7 x 11 x 11 = 213444.

Q24. A Certain Sum Of Money Amounts To Rs.1300 In 2 Years And To Rs. 1525 In three.5 Years. Find The Sum And The Rate Of Interest?

1525-1300= 225 for 1.Five yrs (3.5-2)

so for one yr 225/1.5= 150

then for two yrs interest is 150+a hundred and fifty=300

Then fundamental 1300-three hundred=1000.

Now 150/one thousand*one hundred= 15%.