Weekly income of two persons are in the ratio of 7 : 3 and their weekly expenses are in the ratio of 5 : 2. If each of them saves ? 300 per week, then the weekly income of the first person is?

Let the number be M and N
According to the question.
M/N = 2/3
? 3M = 2N
? 3M - 2N = 0 ...(i)

And (M + 9)/(N + 9) = 3/4
? 4M + 36 = 3N + 27
? 4M - 3N = -9 ...(ii)

Multiplying Ex. (i) by 4 and Eq. (ii) by 3 and subtracting, we get N = 27
Now, putting N = 27 in Eq. (i), we get 3M = 54
? M = 18
? Product of the given numbers = 27 x 18 = 486

Let the smaller number = M and the greater number = N
According to the question ,
(N - M/2) = 4(M - M/2)
? N - M/2 = 4M/2
? N = 2M + M/2
? N = 5M/2
? N : M = 5 : 2

Let the number be 3k and 4k.
According to the question,
(3k + 3)/(4k+ 3) = 4/5
? 5(3k + 3 ) = 4(4k + 3)
? 15k + 15 = 16k + 12
? k = 15 - 12 = 3
? Difference between the numbers = (4k - 3k) = k = 3

Let 1st number = x and 2nd number = y
According to the question 1/2 of x = 65% of y
? x/y = 130/100 = 13/10
? x : y = 13 : 10

Let a + b = 6k, b + c = 7k, c + a = 8k ...(i)
and a + b + c = 14 ...(ii)

From Eq. (i),
a + b + b + c + c + a = 6K + 7K + 8K
? 2(a + b + c) = 21K
? 2 x 14 = 21K
? K = 28/21 = 4/3

? a + b 6k = = 6 x 4/32 = 8
Subtracting Eq. (iii) from Eq. (ii), we get
(a + b + c) - (a + b) = 14 - 8 = 6

Given total amount = ? 49500
Let part of Amit's investment = 4k
and part of sudesh's investment = 7k
According to the question
4k + 7k = 49500
? 11k = 49500
? k = 49500/11
? k = 4500
Hence investment of sudesh = 7k = 7 x 4500 = 31500

Let number of ? 1 coins = 8k
Number of 50 paise coins = 9k
Number of 25 paise coins = 11k

According to the question,
8k + 9k/2 + 11k/4 = 366
? 32k + 18k + 11k = 1464
? 61k = 1464
? k = 1464/61 = 24
? Number of 25 paise coins = 11k = 11 x 24 = 264

Given that P's share : Q 's share = 1/3 : 1/5 = 5 : 3
Here, a = 5, b = 3, N = 1664
P's share = a/(a + b) x N
? = 5/(5 + 3) x 1664 = (5/8) x 1664 = ? 1040

Let the marks of A, B and C are 10k, 12k and 15k, respectively.
Let k = 6
? Maximum marks of C can be = 15 x 6 = 90
So, maximum marks of B can be = 12 x 6 = 72

As the marks are fixed and they cannot exceed the maximum marks.
So, the marks of B cannot be in the range of (80 - 90) ie B cannot score above 80.

let the saving of A and B are 4M , 5M and the share in cost of gift are 3N, 4N respectively
According to the question
for A, 4M - 3N = (2/3) x 4M
? M = 9N/4.............(i)
For B 5M - 4N = 145
? 5 x (9N/4) - 4N = 145 [by Eq. (i)]
? N = 20
? Cost of gift = 3N + 4N = 7 x 20 = ? 140