# Shortcut Rules to Solve Problems on Alligation

## Effective for IBPS PO - SBI PO Exam

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**D****ear Reader **

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**

- The quantity of salt Rs. X per kg that a man must mix with n kg of salt at Rs.y per kg, s that he may, on selling the mixture at Rs.z per kg, gain p % on the outlay is given by

$n\times \left[
\frac{100z-y\left( 100+p \right)}{x\left( 100+p \right)-100z} \right]kg$

**Trick – 2**

- N gm of sugar solution has x % sugar in it. The quantity of sugar should be added to make it y % in the solution is given by n$\left( \frac{y-x}{100-y} \right)gm$, or Quantity of sugar

**Trick – 3**

- A person has a liquid of Rs x per litre. The ratio in which water should we mixed in that liquid, so that after selling the mixture Rs y per litre, he may get a profit of p% is given by

$\left[
\frac{y}{(x-y)+\left( \frac{P}{100} \right)x} \right]$

**Trick - 4**

- A person’s expenditure and savings are in the ration a : b. His income increases by x%. His expenditure also increased by y%. His percentage increase in saving is given by

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

**Trick – 5**

- A trader has N kg of a certain item, a part of which he sells at x% profit and the rest of y% loss. He gain P% on the whole. Then the quantity sold at x % profit is given by $\left[ \left( \frac{P+y}{x+y} \right) \right]kg$ and the quantity sold at y% loss is given by $\left[ \left( \frac{x-P}{x+y} \right)N \right]kg$

**Trick – 6**

- A person travels D km in T hours in two stage. In the first part of the journey, he travels by bus at the speed of x km/hr. In the second part of journey, he travels by train at the speed of y km/hr. Then the distance travelled by bus is $\left[ \frac{yT-D}{y-x} \right]x$ km and the distance travelled by train is $\left[ \frac{D-xT}{y-x} \right]y$ km.

**Questions for Practice****Q1. How many kg of salt at 42 P per kg must a man mix wait 25 kg of salt at 24 P per kg, so that he may, on selling the mixture at 40 P per kg, gain 25% on the outlay ?**

**Q2. 300 gm of sugar solution has 40 % sugar in it. How much sugar should be added to make it 50 % in the solution ?**

**Q3. A person has a chemical of Rs 25 per litre. In what ratio water should we mixed in that chemical, so that after selling the mixture Rs 20 per litre he may get a profit of 25%**

**Q4. Mira’s expenditure and savings are in the ratio 3 : 2. Her income increases by 10%. Her expenditure also increased by 12%. How many % does her saving increases ?**

**Q5. A trader has 50 kg of a rice, a part of which he sells at 10% profit and the rest of 5% loss. He gains 7% on the whole. What is the quantity sold at 10 % gain and 5 % loss ?**

**Q6. A person travels 285 km in 6 hours in two stage. In the first part of the journey, he travels by bus at the speed of40 km/hr. In the second part of journey, he travels by train at the speed of 55 km/hr. How much distance did he travelled by train?**

__Answers__**Answer 1. 20KG**

**Answer 2. 60GM**

**Answer 3. 16: 9**

**Answer 4. 7%**

**Answer 5. 10KG**

**Answer 6. 165KM**

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