Given, 0.764 x P = 1.236 x Q
? Q / P = 1.236 / 0.764
Now, (Q - P) / (Q + P) = [(Q/P) - 1] / [(Q/P) + 1]
? [(1.236/0.764) - 1] / [(1.236/0.764) + 1]
= (1.236 - 0.764) / (1.236 + 0.764)
= 0.472 / 2.000
= 0.236
Then, unit's digit = x + 2.
Number = 10x + (x + 2) = 11x + 2.
Sum of digits = x + (x + 2) = 2x + 2.
∴ (11x + 2)(2x + 2) = 144
⟹ 22x2 + 26x - 140 = 0
⟹ 11x2 + 13x - 70 = 0
⟹ (x - 2)(11x + 35) = 0
⟹ x = 2.
Hence, required number = 11x + 2 = 24.
Let the given number be N
Therefore N = 357k + 39
Then,
357 k + 39 = ( 17 x 21k ) + ( 17 x 2 ) + 5
? Required remainder = 5
(1/2)x | + | (1/2)x | = 10 |
21 | 24 |
⟹ | x | + | x | = 20 |
21 | 24 |
⟹ 15x = 168 x 20
⟹ x = | ❨ | 168 x 20 | ❩ | = 224 km. |
15 |
We know that, when a pipe fills a tank in m h, then the part of tank filled in 1 h = 1/m
Here, m = 6
? Required part of the tank to be filled in 1h = 1/6 part
Then, 2x = 10 or x = 5. So, the number is either 253 or 352.
Since the number increases on reversing the digits, so the hundred's digits is smaller than the unit's digit.
Hence, required number = 253.
7429 Let 8597 - x = 3071 -4358 Then, x = 8597 - 3071 ---- = 5526 3071 ----
Work done by leak in 1 hour = (1/8 - 1/10) = 1/40
? The leak will empty the cistern in 40 hours.
Total persons on the circular table
= 20 guests + 1 host = 21
They can be seated in (21 - 1) ! = 20 ! ways .
Time taken by the pipe to empty the cistern = 3 h
Then, time taken by the pipe to empty the 2/3 part = 3 x 2/3 = 2 h
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