If the number 653 xy is divisible by 90, then (x + y) = ?

Question: Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
[A].

Rs. 169.50

[B].

Rs. 170

[C].

Rs. 175.50

[D].

Rs. 180

Answer: Option C

Explanation:

Since first and second varieties are mixed in equal proportions.

So, their average price = Rs.		126 + 135		= Rs. 130.50
		2

So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.

By the rule of alligation, we have:

Cost of 1 kg of 1st kind Cost of 1 kg tea of 2nd kind
Rs. 130.50	Mean Price Rs. 153	Rs. x
(x – 153)		22.50

	x – 153	= 1
	22.50

x – 153 = 22.50

x = 175.50

Question:
In what ratio must water be mixed with milk to gain 16% on selling the mixture at cost price?

[A].

1 : 6

[B].

6 : 1

[C].

2 : 3

[D].

4 : 3

Answer: Option A

Explanation:

Let C.P. of 1 litre milk be Re. 1.

S.P. of 1 litre of mixture = Re.1, Gain =	50	%.
	3

C.P. of 1 litre of mixture =		100 x	3	x 1		=	6
			350				7

By the rule of alligation, we have:

C.P. of 1 litre of water C.P. of 1 litre of milk
0	Mean Price Re. 6 7	Re. 1
1 7		6 7

Ratio of water and milk =	1	:	6	= 1 : 6.
	7		7