While A scores 90 points, B scores (90-15)=75 points and C scores (90-30)= 60 points
i.e., when B scores 75 points, C scores 60 points
=> When B scores 100 points, C scores 6075×100 = 80 points
i.e., in a game of 100 points, B can give C (100-80)=20 points
Let the numbers be 37a and 37b.
Then, 37a x 37b = 4107
ab = 3.
Now, co-primes with product 3 are (1, 3).
So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).
Greater number = 111.
Required number = H.C.F. of (1657 - 6) and (2037 - 5)
= H.C.F. of 1651 and 2032 = 127.
20 * 10 * 5 = 1000
6 dozen apples = Rs. (12 × 4 + 16 × 2) = Rs. 80
Gain = 20%
S.P = Rs. (120/100 × 80) = Rs. 96
Per dozen = Rs. (96/6) = Rs. 16
Let the quantity of alcohol and water be 4x litres and 3x litres respectively
4x/(3x+5) = 4/5
20x = 4(3x+5)
8x = 20
x = 2.5
Quantity of alcohol = (4 x 2.5) litres = 10 litres.
Speed downstream = (13 + 4) km/hr = 17 km/hr.
Time taken to travel 68 km downstream =68/17hrs = 4 hrs.
Perimeter = Distance covered in 8 min. =12000x 8m = 1600 m.
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m2.
Let event A = Sam wins and event B = Joan wins. Then,
P(A) = 0.59
Since if Sam wins, Joan cannot win and if Joan wins, Sam cannot win, so we can say that the events A and B are mutually exclusive. Other than these two events, there are
no any other possible outcomes. So,
P(A)+P(B) = 1
0.59+P(B) = 1
P(B) = 1-0.59 = 0.41
Average = total runs / no.of innings = 32
So, total = Average x no.of innings = 32 x 10 = 320.
Now increase in avg = 4runs. So, new avg = 32+4 = 36runs
Total runs = new avg x new no. of innings = 36 x 11 = 396
Runs made in the 11th inning = 396 - 320 = 76
Speed = 600/ 5 x 60 m/sec. = 2 m/sec. = 2 x 18/5km/hr =7.2 km/hr
Rate of consumption of each man = 1050/(150 * 30) = 7/30 kg/day
Let us say 70 men take x days to consume 150 kg.
Quantity consumed by each item in x days = (7x/30) kg
Quantity consumed by 70 men in x days = (7/30 x)(70) kg
= (7/30 x) * (70) = 960
x = 60 days.
first we need to calculate 1 hours work, then their collective work as A's 1-hour work is 1/8
B's 1-hour work is 1/10
(A+B)'s 1 hour work = 1/8 + 1/10= 9/40
So both will finish the work in 40/9 hours=4 4/9
we first get the filling in 1 minute for both pipes then we will add them to get the result, as
Part filled by A in 1 min = 1/20
Part filled by B in 1 min = 1/30
Part filled by (A+B) in 1 min = 1/20 + 1/30= 1/12
So both pipes can fill the tank in 12 mins.
C’s 1 day’s work = 1/3 – (1/6 + 1/8) = 1/3 – 7/24 = 1/24
A’s wages : B’s wages : C’s wages
1/6 : 1/8 : 1/24 = 4:3:1
C’s share = 1/8 * 3200 = Rs. 400
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.
Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 – 399) = 9600.