In how many ways can 6 boys and 5 girls be seated in a row so that no two of the girls sit together ?
7! 6!/2! 6 boys can be seated in a row in 6! ways. x B x B x B x B x B x B x
If girls sit at the place indicated by x then no two girls will still together.
Now their are 7 places for 5 girls so they can be seated in 7P5 ways.
∴ Reqd no. of total ways = 7P5 x 6! = 7! x 6!/2!
What is the change that a leap year selected randomly will have 53 Mondays ?
A leap year has 366 days. So it has 52 weeks and 2 more days. The two days can by any 7 pairs like Monday-Tuesday and Tuesday-Wednesday
ie n(S) = 7
Out of these 7 pairs, 2 pairs contain Monday: they are Monday-Tuesday and Sunday-Monday.
∴ n(E) = 2
∴ P(E) = n(E)/n(S) = 2/7
A man can row 10km/h in still water. If the river is running at 3 km/h, it takes 6 hours more to go upstream than downstream for the same distance. How far is the place in km ?
Let the distance be x
∴ x/10-3 - x/10+3 = 6
∴ x = 91 km
∴ x/7 - x/13 = 6
∴ 13x - 7x/91 = 6
Two trains of length 100m and 120 m respectively with different speeds pass a pole in 5 sec and 10 sec respectively. In what time will they cross each other when they are moving in the same direction ?
Speed of 1st train = 100/5 = 20ms-1
Speed of 2nd train = 120/10 = 12 ms-1
In the same distance their relative speed
20 - 12 = 8 ms-1
Total distance = 100 + 120 = 220 m
∴ Time = 220/8 = 55/2 = 27.5 sec
If Rs 600 becomes Rs 3600 in 20 years on a simple interest rate 'R*, then what is the rate of interest (value of R) ?
Here sum is 600. After 20 yrs it is 3600.
∴ Interest = 3600 - 600 = 3000.
∴ Rate of interest = 100 x 3000/600 x 20 = 25%
The simple interest on a certain sum of money for 2 years at 8% per annum is Rs 2200. What will be the compound interest at the same rate and for the same time ?
CI = r + 200/200 x S = 208/200 x 2200 = 2288
A man 'A' can do a work in 30 days. With the help of another man" B' he can do the same work in 17 days. If they get Rs 2100 for that work, what is the share o f ' B ' ?
A will do 17/30 work in 17 days.
= B will do 1-17/30 = 13/30 work, in 17 days.
Therefore, ratio of their shares should be
A : B = 17 : 13
∴ B's share = 2100/(17+13) x 13 = 910
If a men can do 3/5 of a work in 18 dsays, how many days will he take to finish 2/5 of the work ?
x/3/5 = y/2/5; Hence x = 18
∴ y = 5x/3 x 2/5 = 10x18/15 = 180/15 = 12.
The sum of the ages o f ' A ' and ' B ' is 80 years. After 20 years the age of 'A' is twice that of ' B ' . What is the present age o f ' B ' in years ?
Let their ages be x and y
∴ x + y = 80....(i)
x + 20/y + 20 = 2 ie x - 2y = 20 ......(ii)
Solving (i) and (ii), we get x = 60 and y = 20
∴ B's age = 20 yrs.
A dishonest dealer sells his goods at the cost price, but he uses a weight of 900 gm for 1 kg wt. What is his gain per cent ?
Suppose the cost of the item is Re 1 per kg. So he sells for Re 1 what cost him Re 0.90
∴ gain = 1.0.9 = 0.1
∴ gain on Rs. 100 = 0.1/0.9 x 100 = 100/9 = 11 1/9%
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