Let the money at 10% be Rs. P, Then the money at 9% is Rs. (2600 - P )
? (P x 10 x 5)/100 = [(2600 - P ) x 9 x 6]/100
or 104 x P = 2600 x 54
or P = (2600 x 54) / 104 = Rs.1350
Given , X = ?3 + ?2
? 1/x = 1/(?3 + ?2)
Now Multiply and Divide by (?3 - ?2) in 1/x.
After multiply and divide, we will get
1/x = (1/(?3 + ?2)) X (?3 - ?2) /(?3 - ?2)
[rationalising]
? 1/x = ?3 - ?2/3 - 2
? x + 1/x = ?3 + ?2 + ?3 - ?2 = 2?3
Rate percent = 100 x 2/5/ [ 3/(23 - 3)] = 6%
Let us draw a figure as per given question.
Let AB = 5 meter and CD = 2 meter be the heights of a lamp post and the men respectively.
At any time t BD = x meter and shadow of man ED = y meter.
Then, dx/dt = 6 m/min
Now, right triangles ABE and CDE are similar, then
AB/CD = BE/DE
? 5/2 = (x + y)/y
? 5y = 2x + 2y
? 5y - 2y = 2x
? 3y = 2x
? 3 dy/dt = 2 dx/dt
? 3 dy/dt = 2 x 6
? dy/dt = 2 x 6 / 3
? dy/dt = 2 x 2 = 4
Hence, length of his shadow increase at the rate of 4 m/min.
Number of pages typed by Ravi in 1 hour = | 32 | = | 16 | . |
6 | 3 |
Number of pages typed by Kumar in 1 hour = | 40 | = 8. |
5 |
Number of pages typed by both in 1 hour = | ❨ | 16 | + 8 | ❩ | = | 40 | . |
3 | 3 |
∴ Time taken by both to type 110 pages = | ❨ | 110 x | 3 | ❩ | hours |
40 |
= 8 | 1 | hours (or) 8 hours 15 minutes. |
4 |
Let total score = N.
Then, the highest score = 3N/11.
Remainder = (N - 3N/11) = 8N/11
Next highest score = 3/11 of 8N/11 = 24N/121
According to the question,
(3N/11) - (24N/121) = 18
? 33N - 24N = 18 x 121
? 9N = 18 x 121
? N = (18 x 121)/9 = 242
∴ (2x + 2) + 2x + x = 27
⟹ 5x = 25
⟹ x = 5.
Hence, B's age = 2x = 10 years.
Then, 5 : 8 : 15 : x
⟹ 5x = (8 x 15)
x = | (8 x 15) | = 24. |
5 |
We know that, (a + b)2 = a2 + b2 + 2ab
= 234 + 2 x 108 = 450
(a - b)2 = a2 + b2 - 2ab
= 234 - 2 x 108 = 18
? (a + b)2/(a - b)2 = 450/18 = 25
? [(a + b)/(a - b)]2 = 25
? (a + b)/(a - b) = ?25 = 5
32 | 8 | min. |
11 |
36 | 5 | min. |
11 |
32 | 8 | min. |
11 |
60 min. spaces are covered in | ❨ | 60 | x 60 | ❩min. | = 65 | 5 | min. |
55 | 11 |
Loss in 64 min. = | ❨ | 65 | 5 | - 64 | ❩ | = | 16 | min. |
11 | 11 |
Loss in 24 hrs = | ❨ | 16 | x | 1 | x 24 x 60 | ❩min. | = | 32 | 8 | min. |
11 | 64 | 11 |
x = 13200 - 9873 = 3327
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