We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ?P? ways.
Hence required number of ways = 6! x ?P?
The banker's gain on a certain sum due 1 | 1 | years hence is | 3 | of the banker's |
2 | 25 |
discount. The rate percent is:
5 | 1 | % |
5 |
9 | 1 | % |
11 |
8 | 1 | % |
8 |
6 | 1 | % |
6 |
9 | 1 | % |
11 |
Then, B.G. = Re. | 3 | . |
25 |
∴ T.D. = (B.D. - B.G.) = Re. | ❨ | 1 - | 3 | ❩ | = Re. | 22 | . |
25 | 25 |
Sum = | ❨ | 1 x (22/25) | ❩ | = Rs. | 22 | . |
1-(22/25) | 3 |
S.I. on Rs. | 22 | for 1 | 1 | years is Re. 1. |
3 | 2 |
∴ Rate = | ❨ | 100 x 1 | ❩% |
|
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Total number of marbles = 6 + 4 + 2 + 3 = 15
Ways of selection of two red marbles = n(E) = 6C2
Ways of selection of two marbles = n(S) = 15C2
So, required probability = (6C2) / (15C2)
= (6 x 5) / (15 x 14) = 1/7
4 | A | = | 2 | B | |
15 | 5 |
⟹ A = | ❨ | 2 | x | 15 | ❩B |
5 | 4 |
⟹ A = | 3 | B |
2 |
⟹ | A | = | 3 |
B | 2 |
⟹ A : B = 3 : 2.
∴ B's share = Rs. | ❨ | 1210 x | 2 | ❩ | = Rs. 484. |
5 |
Part of the tank filled in 1 min by A, B and C = 1/20 + 1/15 +1/12
= (3 + 4 + 5)/60 = 12/60 = 1/5
? Time taken by A, B and C to fill the tank = 5 min
? Time taken by A, B and C to fill 40% of the tank = 40% of 5 = (40/100) x 5 = 2 min.
0.252525 ..... = 0.25= 25/99
Given ratio = 1/3 : 1/4 : 1/5 = 20 : 15 : 12
Let length of the sides be 20k, 15k and 12k.
Then, according to the question,
20k + 15k + 12k = 94
? 47k = 94
? k = 94/47 = 2
Smallest side = 12k = 12 x 2 = 24 cm
Average salary
= 8000 + 5000 + 11000 + 7000 + 9000 / 5
= Rs. 8000
Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131.
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138 + 2 x 131 = 400.
⟹ (a + b + c) = √400 = 20.
Let the sum borrowed = P
Then, according to the question,
[(P x 6 x 3)/100] + [(P x 9 x 5)/100] + [(P x 13 x 3)/100] = 8160
? (18P + 45P +39P) / 100 = 8160
? 102P/100 = 8160
? P = (8160 x 100)/102
? P = ? 8000
Then, distance covered = 2x metres.
Relative speed = (46 - 36) km/hr
= | ❨ | 10 x | 5 | ❩m/sec |
18 |
= | ❨ | 25 | ❩m/sec |
9 |
∴ | 2x | = | 25 |
36 | 9 |
⟹ 2x = 100
⟹ x = 50.
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