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A 60% spirit solution is mixed with r% spirit solution in the ratio 1 : 3 such that a s% spirit solution is obtained. When a (s/3)% spirit solution is mixed with 55% spirit solution in equal ratio, an (r/2)% spirit solution is obtained. Which of the following can be determined? (A) Value of ‘r’ (B) Value of ‘s’ (C) Volume of the 60% spirit solution mixed initially (D) If 9 liters of r% spirit solution was mixed initially, what was the volume of the s% spirit solution thus obtained?
A chemical solution appears green when the salt concentration is 8 grams per litre (gpl) and red when it is 10 gpl. Pure water was added to the solution of 1 litre of 15 gpl solution till it turned green. Then 125 ml of the green solution is taken out and x grams of salt is added to the green solution to make it red. Another 500 ml of the final solution was taken out and y litres of green solution is added to get a resultant solution of concentration 9.6 gpl.  Assume adding salt doesn’t change its volume and find the ratio of x and y. 
The linear congruence ax ≡ b(mod n) has a solution if and only if,
Choose the linear congruence which has exactly 3 solution modulo 3
The system of linear congruence x ≡ ai (mod ni) with gcd(ni, nj) = 1 for i ≠ j has a simultaneous solution which is 
Consider a linear congruence a ≡ b (mod m), Choose the false relation from the option given below:
Solution X contains 7% (by weight) of liquid M and solution Y contains 14.5% (by weight) of liquid M. If 3 grams of solution X is mixed with 2 grams of solution Y, then liquid M accounts for what percent of the weight of the resulting solution?
100 kg of solution A is mixed with 60 kg of solution B . If solution A has tin and copper in the ratio 1: 4 and solution B has lead and tin in the ratio 3 :2 then what is the amount of tin in the new solution?
Solution X is 10% percent alcohol by volume, and solution Y is 30 percent alcohol by volume. How many milliliters of solution Y must be added to 200 milliliters of solution X to create a solution that is 25 percent alcohol by volume?
What happens when a solution of an acid is mixed with a solution of a base in a test tube? (i) The temperature of the solution increases. (ii) The temperature of the solution decreases. (iii) The temperature of the solution remains the same. (iv) Salt formation takes place.