L.C.M. of 21, 36, 66 = 2772 Now,
2772 = 2 x 2 x 3 x 3 x 7 x 11 To make it a perfect square,
it must be multiplied by 7 x 11. So,
required number = 2 x 2 x 3 x 3 x 7 x 7 x 11 x 11 = 213444.
We need to find out the HCF for given length.
15 meter 75 cm = 1575 cm.
11 meter 25 cm = 1125 cm 7 meter 65 cm = 765 cm.
1575 = 5 *5 *3 *3 *7 1125 = 5 *5 *5 *3 *3 765.
= 5 *3 *3 *17 HCF of 1575, 1125 and 765 is 45 (5 *3*3).
log2x = 10 ⇒ x = 210.
∴ logx y = 100
⇒ y = x100
⇒ y = (210)100 [put value of x]
⇒ y = 21000.
Given Exp= log75/16 – 2 log5/9 + log32/343
= log [(25 x 3) / (4 x 4)] – log (25/81) + log [(16 x 2) / (81 x 3)]
= log(25 x 3) – log ( 4 x 4 ) – log(25) + log81 + log(16 x 2) -log (81 x 3)
= log 25 + log 3 – log 16 – log 25 + log 81 + log 16 + log 2 – log 81 – log 3
= log 2.
Rewrite the equation as x=log2(164)x=log2(164).
x=log2(164)x=log2(164) Logarithm base 22 of 164164 is −6-6.
Distance = 110 m
Relative speed = 60 + 6 = 66 kmph
(Since both the train and the man are in moving in opposite direction) = (66*5/18) m/sec = 55/3 m/sec.
Let the total 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.
Here as per condition let us consider third number = x,
then 2nd number = 2x and 3rd number = 4x,
Given that (4x+2x+x)/3 = 77,
7x = 3×77, x = 3 x 11 = 33,
first number = 4x = 4 x 33 = 132.
Let the cost price be 100%. It is sold at 10% loss.
So it is sold at 90% of the cost price.
90 % of the cost price + 450 = 108% of the Cost price 18% of the cost price = Rs 450 Cost price of the book = 450/18 x 100 = Rs 2500.
1525-1300= 225 for 1.5 yrs (3.5-2)
so for one yr 225/1.5= 150
then for 2 yrs interest is 150+150=300
Then principal 1300-300=1000.
Now 150/1000*100= 15%.
Question 11. The Mean Daily Profit Made By A Shopkeeper In A Month Of 30 Days Was Rs. 350. If The Mean Profit For The First Fifteen Days Was Rs. 275, Then The Mean Profit For The Last 15 Days Would Be?
Find the total profit made in the first 15 days:
Mean daily profit for the first 15 days = Ra 275
Total profit for the first 15 days = 275 x 15 = Rs 4125.
Find the total profit for the last 15 days:
10,500 - 4125 = Rs 6375.
Find the mean profit for the last 15 days:
Mean profit = 6375 ÷ 15 = Rs 425.
Question 12. There Were 35 Students In A Hostel. If The Number Of Students Increases By 7, The Expenses Of The Mess Increase By Rs. 42 Per Day While The Average Expenditure Per Head Diminishes By Re 1. Find The Original Expenditure Of The Mess?
Let d be the average daily expenditure
Original expenditure = 35 × d
New expenditure = 35 × d + 42
New average expenditure will be :
(35 × d + 42)/42 = d - 1
On solving, we get d = 12
Therefore original expenditure = 35 × 12 = 420.
Question 13. 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 : 1. If On A Particular Day Rs. 1,325 Were Collected From The Passengers Travelling Between These Stations, Then What Was The Amount Collected From The Ii Class Passengers?
Let x be the number of passengers and y be the fare taken from passengers.
3xy + 50xy = 1325 => xy = 25
Amount collected from II class passengers = 25 × 50 = Rs. 1250.
Question 14. A Pump Can Be Operated Both For Filling A Tank And For Emptying It. The Capacity Of The Tank Is 2400 M3. The Emptying Capacity Of The Pump Is 10m3 Per Minute Higher Than Its Filling Capacity. Consequently, The Pump Needs 8 Minutes Less To Empty The Tank Than To Fill It. Find The Filling Capacity Of The Pump?
Let the filling capacity 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 needs 8 minutes lesser to empty the tank than it needs to fill it
x = 50 or -60
Since x can not be negative, x=50
i.e.,filling capacity of the pump = 50 m3/min.
A can give B a 100 m start and C a 150m.
Start means 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. 8500/9 m) Thus,
B can give C a start of - 1000 - (8500/9), i.e. 500/9 m.
Question 16. 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 Number Of Boys In The Class?
Let Boys in class = B
Girls in class = 20
Now, (20B+15*20)/(B+20) = 18
⇒ B = 30.
Question 17. 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 Speed?
Let the speed of goods train be x km/hr.
(50+x)×( 5 18 )= 187.5 9
⇒ x= 25 km/hr.
Distance = Speed × time
Here time = 2hr 45 min = 114 hr
Distance = 4×114=11 km
New Speed =16.5 kmph
Therefore time = DS=1116.5=40 min.
Time = 50/60=5/6 hr
Speed = 48 mph
Distance = S×T=48×5/6=40 km
Time = 40/60 hr
New speed = 40×3/2=60 kmph.
Let the normal speed be 's' km/hr
Then new speed = (s+5) km/hr
On solving this equation we get:
s = 25 km/hr.
Question 21. 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 Train Completely In 60 Sec. Whereas A Passenger On The Passenger Train Marks That He Crosses The Goods Train In 40 Sec. If The Speeds Of The Trains Be In The Ratio 1:2. Find The Ratio Of Their Lengths?
Let the speeds of the two trains be s and 2s m/s respectively.
Also, suppose that the lengths of the two trains are P and Q metres respectively.
On dividing these two equation we get:
P:Q = 2 : 1.
Question 22. 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 And By How Much?
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 396/400×395=391.05m
If C covers 391.05 m, then D will cover 400/384×391.05=407.24
If A and D run over 400 m, then D win by 7.2 m (approx.)
Question 23. 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 3.75 Km/hr Respectively. They Will Meet For The First Time In?
et both of them meet after T min
4500 m are covered by Suresh in 60 m.
In T min he will cover 4500T60
Likewise, In T min Suresh's wife will cover 3750T60
Question 24. 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 11:30 Am, If The Distance Between Delhi And Ambala Cantt Is 200 Km, Then At What Time Did The Two Trains Meet Each Other?
Average speed of train leaving Delhi = 2004=50 km/hr
Average speed of train leaving Ambala cantt. = 200×27=4007
By the time the other train starts from Ambala cantt, the first train had travelled 100 km
Therefore, the trains meet after:
Hence they meet at 8:56 am.
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