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.