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**Statement based simplification**

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# Statement based Simplification

When you are acquainted with the concepts of Statement based Simplification or arithmetic reasoning, you will be able to easily solve any question. The AR questions do not involve complex calculations rather the questions tend to play with your mind with the tricky concept and language. You can practice the questions easily by using simple mathematical operations, arithmetic operations etc.

## Simplification Topics

Listed below are the main topics under Arithmetic Reasoning-

- Ratio and Proportion
- Percentage
- Square/ squareroot
- HCF and LCM
- Ages
- Games and Tournaments
- Sequence and Patterns

**Examples:**

Now let us go through some solved examples to understand the concept in a better way.

**Example 1:** Riya is 2 times older than Priya. 3 years ago, the sum of their current ages will be 66. What are their present ages?

**Solution:**

Let us begin by assuming their ages

Assume that Riya’s age is x

Its is given that the Priya is twice as old as Riya, then, Priya’s age will be 2x

After 3 years,

Riya’s age= x + 3

Priya’s age= 2x + 3

Their total sum is 66

Hence, the equation becomes,

x+ 3 + 2x + 3= 66

3x + 6 = 66

3x= 66- 6

3x = 60

x= 60/ 3

x= 20

So, the age current age of Riya is 20 and that of Priya is 40

**Example 2**: Find the number which when multiplied by 3/4th of itself gives out the value 10800.

**Solution:**

Let us begin by assuming that the number is y

Then 3/4th of y would be (y x 3/4)

As per the question,

y x (y x 3/4) = 10800

3/4 x y ^{2}= 10800

y ^{2}= 10800 x 4/3

y ^{2}= 14400

y = 14400

y = 120

**Example 3:** Rahul is now 1/4th times as old as his mother Radha. Four years hence, his mother will be three times as old as her son. The age of his mother Radha (in years) is-

**Solution**: Let Rahul’s mother Radha age be 4x years. Then, Rahul’s age = x years.

Four years hence, Rahul’s age = (x + 4) years and Rahul’s mother Radha’s age = (4x + 4) years.

So, 4x+4= 3 (x+4)

4x-3x= 12-4;

x = 8.

Rahul’s mother Radha’s age = 4x= 4 x 8=32 years

**Example 4**: A monkey climbs 30 feet at the beginning of each hour and rests for a while when he slips back 20 feet before he again starts climbing at the beginning of the next hour. If he begins his ascent at 8.00 a.m., at what will he first touch a flag at 120 feet from the ground?

**Solution**: Let ascent of the monkey in 1 hour = ( 30 – 20 ) = 10 feet.

So, the monkey ascends 90 feet in 9 hours i.e., 5 p.m.

Clearly, in the next 1 hour i.e., till 6 p.m.

The monkey ascends the remaining 30 feet to touch the flag.

**Example 5**: Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A?

**Solution: **

Let Rs. x be the fare of city B from city A and Rs. y be the fare of city C from city A. Then,

2x + 3y = 77 …(i)

3x + 2y = 73 …(ii)

Multiplying (i) by 3 and (ii) by 2 and subtracting, we get: 5y = 85 or y= 17. Putting y = 17 in (i), we get : x = 13

**Example 6:** A girl counted in the following way on the fingers of her left hand: She started by calling the thumb 1, the index finger 2, middle finger 3, ring finger 4, little finger 5 and then reversed direction calling the ring finger 6, middle finger 7 and so on. She counted up to 1994. She ended up counting on which finger?

**Solution: **While counting the numbers associated to the thumb will be 1,9,17,25,………

i.e., numbers of the form (8n + 1 )

Since 1994 = 249 × 8 + 2

So, 1993 shall correspond to the thumb and 1994 to the index finger.

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