Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?

A : B =

[

4x x 3 +

❨

4x -

1

x 4x

❩

x 7

]

:

[

5x x 3 +

❨

5x -

1

x 5x

❩

x 7

]

4

5

   = (12x + 21x) : (15x + 28x)

   = 33x :43x

   = 33 : 43.

∴ A's share = Rs.	❨	760 x	33	❩	= Rs. 330.
			76

For managing, A received = 5% of Rs. 7400 = Rs. 370.

Balance = Rs. (7400 - 370) = Rs. 7030.

Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)

   = 39000 : 42000 : 30000

   = 13 : 14 : 10

∴ B's share = Rs.	❨	7030 x	14	❩	= Rs. 2660.
			37

Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.

Then, 14x : 8y : 7z = 5 : 7 : 8.

Now,	14x	=	5	⟺    98x = 40y    ⟺    y =	49	x
	8y		7		20

And,	14x	=	5	⟺    112x = 35z    ⟺    z =	112	x =	16	x.
	7z		8		35		5

∴ x : y : z = x :	49	x	:	16	x	= 20 : 49 : 64.
	20			5

Let C = x.

Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.

So, x + x + 5000 + x + 9000 = 50000

⟹ 3x = 36000

⟹ x = 12000

A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.

∴ A's share = Rs.	❨	35000 x	21	❩	= Rs. 14,700.
			50

Suppose B joined for x months. Then,

Then,	❨	85000 x 12	=	3	❩
		42500 x x		1

⟹ x =	❨	85000 x 12	❩	= 8.
		42500 x 3

So, B joined for 8 months.

Let the mother's present age be x years.

Then, the person's present age =	❨	2	x	❩	years.
		5

∴	❨	2	x + 8	❩	=	1	(x + 8)
		5				2

⟹ 2(2x + 40) = 5(x + 8)

⟹ x = 40.

Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.

Then,	(6x + 6) + 4	=	11
	(5x + 6) + 4		10

⟹ 10(6x + 10) = 11(5x + 10)

⟹ 5x = 10

⟹ x = 2.

∴ Sagar's present age = (5x + 6) = 16 years.

Given that:

1. The difference of age b/w R and Q = The difference of age b/w Q and T.

2. Sum of age of R and T is 50 i.e. (R + T) = 50.

Question: R - Q = ?.

Explanation:

R - Q = Q - T

(R + T) = 2Q

Now given that, (R + T) = 50

So, 50 = 2Q and therefore Q = 25.

Question is (R - Q) = ?

Here we know the value(age) of Q (25), but we don't know the age of R.

Therefore, (R-Q) cannot be determined.

Let the present ages of Sameer and Anand be 5x years and 4x years respectively.

Then,	5x + 3	=	11
	4x + 3		9

⟹ 9(5x + 3) = 11(4x + 3)

⟹ 45x + 27 = 44x + 33

⟹ 45x - 44x = 33 - 27

⟹ x = 6.

∴ Anand's present age = 4x = 24 years.

Let the ages of father and son 10 years ago be 3x and x years respectively.

Then, (3x + 10) + 10 = 2[(x + 10) + 10]

⟹ 3x + 20 = 2x + 40

⟹ x = 20.

∴ Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.