# Shortcut Rules to Solve Problems on ALLIGATION

## Effective for IBPS PO - SBI PO Exam

Here we will start a series of Quantitative Aptitude Shortcut Tricks for your upcoming SBI - IBPS - SSC and Other Government Competitive Exams. We will try to cover up all topics of the quantitative Aptitude Sections from which question was generally asked.

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Trick - 1
• 'L' litres are drawn from a cask full of water and it is filled with milk. After n operations, if the quantity of water now left in the cask is to that of milk in it as a:b, then the capacity of cask is given by
$\left[ \frac{L}{1-{{\left( \frac{a}{a+b} \right)}^{{}^{1}/{}_{n}}}} \right]litres$

Trick - 2
• If a person buys n kg of an item at the rate of Rs. P per kg. If he sells m kg at a profit off x% then the rate per kg, at which he should sell the remaining to get a profit of y% on the total deal, is given by

Rs. $P\left[ 1+\frac{ny-mx}{(n-m)100} \right]$

Trick - 3
• A man mixes ${{M}_{1}}$ litres of milk at Rs.x per litre with ${{M}_{2}}$ litres at Rs. y per litre. Amount of water, that should be added to make the average value of the mixture Rs. z per litre, is given by

$\left[ \frac{{{M}_{1}}(x-z)+{{M}_{2}}(y-z)}{z} \right]litres$
Trick - 4
• L litres of a mixture contains two liquids A and B in the ratio a:b. The amount of liquid B, that is added to get a new mixture containing liquid A and B in the ratio x,y is given by

$\left[ \left( \frac{\frac{y}{x}}{1+\frac{b}{a}} \right)-\left( \frac{1}{1+\frac{a}{b}} \right) \right]L$ litres.

Trick -5
•  If M kg of mixture, of which $\frac{a}{b}$ is A and the rest is B, be mixed with N kg of metal, of which $\frac{x}{y}$ is A and the rest is B in the mixture is given by

$\left[ \frac{M\frac{a}{b}+N\frac{x}{y}}{M\left( 1-\frac{a}{b} \right)+N\left( 1-\frac{x}{y} \right)} \right]$

Trick -6

• There are 'N' students in a class. Rs. X are distributed among them so that each boy gets Rs.x and each girl gets Rs.y. Then the ratio of boys to the girl is fiven by $\left[ \frac{X-Ny}{Nx-X} \right]$ and the no. of boys and the no. of girls are $\left( \frac{X-Ny}{x-y} \right)$  and $\left( \frac{Nx-X}{x-y} \right)$ respectively.

Questions for Practice

Q1. Nine litres are drawn from a cask full of water and it is filled with milk. Nine litres of mixture are drawn and the cask is again filled with milk. The quantity of water now left in the cask is to that of milk in it as 16:9. How much does the cask hold ?

Q2. Jayshree purchased 150 kg of wheat at the rate of Rs. 7 per kg. She sold 50 kg at a profit of  10%. At what rate per kg should she sell the remaining to get a profit of 20% on the total deal,

Q3. A man mixes 5 kilolitres  of milk at Rs.600 per kilolitre with 6 kilolitres at Rs. 540 per kilolitre  of water should be added to make the average value of the mixture Rs. 480 per kilolitre ?

Q4. 729 litres of a mixture contains milk and water in the ratio 7:2. How much water is added to get a new mixture containing milk and water in the ratio 7:3

Q5. If 2 kg of metal, of which $\frac{1}{3}$ is zinc and the rest of copper, be mixed with 3 kg of metal, of which $\frac{1}{4}$ is zinc and the rest is copper, what is ratio of zinc to copper in the mixture ?

Q6. There are 65 students in a class 39 rupees are distributed among them so that each boy gets 80 P and each girl gets 30 P. Find the number of boys and girls in that class.