S NAGA MALLESWARA REDDY

March 2016

Aptitude - Ages

Solving problems on ages is a two step process.

Create linear equations based on statements provided.
Solve the equations to get the values as required ages.

Solved Examples

Q 1 - If the ratio of ages of two persons Ram and sham is 5:4 . After Three years their age ratio changes and becomes 11:9. In that case tell about the present age of mr. sham.

Answer - B

Explanation

If the age of Mr. Ram  5x and 4x is the age of Mr. sham.  Then, ( 5x+3) /( 4x+3) = 11/9  ⇒ 9 (5x+3)= 11 (4x+3) ⇒ x= (33-27) = 6  So the present age of Mr. sham = 6*4 = 24 years.

Q 2 - A mother is 30 time older in the comparison of her daughter. After the period of 18 year , the mother age would be thrice in the comparison of his daughter . In that case tell about the present age of mother.

Answer - A

Explanation

Let  daughter present age   be  x year .  in that case mother  present age would be = 30x years    30x+ 18 = 3 (x+ 18) ⇒ 27x = 36  ⇒ x = 4/3    ∴ so the present age of mother = (30* 4/3) = 40 years.

Q 3 - The ratio of present ages of three persons ajay , vijay and sanjay are in the proportion of 4: 7: 9. Before 8 year total sum of their age is 56. What should be the present ages?

Answer - A

Explanation

If the present age of ajay , vijay and sanjay is  4x , 7x and 9x years.  Total sum of  ages of ajay, vijay and sanjay  before 8 years  ago = (4x-8)+(7x-8)+(9x-8)  =(20x-24) years.  ∴ 20x-24 = 56 ⇒ 20x = 80 ⇒ x= 4   Hence,  it proves that age of ajay is 4*4 = 16 years,   vijay (7*4) = 28 years  and sanjay  (9* 4) = 36 years.

Q 4 - Daughter's present age is 2/5 in the comparison of her mother .8 year later , age of her daughter will be 1/2 in the comparison of her mother. Find out mother present age?

Answer - B

Explanation

If the present age of mother is  equal to  x year.    In that situation the daughter present age would be = 2x/5 years.  2x/5 + 8 = 1/2 (x+8) ⇒  4x+ 80 = 5x+40 ⇒ x = 40.  The mother age at the present time is = 40 years.

Q 5 - Ajay age was double in the comparison of bhuvan before 3 years. Seven years hence, the sum of both ages would be 83 years. What should be the age at the present time of both?

Answer - C

Explanation

Before  3 year  let  bhuvan age be x years.   3 years before , ajay age will be  2x years.   Now Bhuwan's  age =(x+3) years and ajay  age = (2x+3) years.  (x+3)+7+(2x+3)+7 = 83 ⇒  3x+20 = 83 ⇒ 3x = 63 ⇒ x = 21   Now the bhuwan present age = (21+3) = 24 years   Now the ajay present age = (2 *21+3) years = 45 years.

Q 6 - I am 4 year older in the comparison of my sister, but my brother who is the youngest among us is 7 year younger to myself. My father is three times in the comparison of my brother. The present age of my sister 18 year and my father is 3 year older in the comparison of my mother. In that situation what should be the present age of my mother?.

Answer - A

Explanation

If my sister age is x years. Then,  Sister  -    x   I   -       x+4  Brother -  (x+4-7) = x-3  Father - 3 (x-3)   Given x = 18  ∴  Father's age =  3(18-3) = 45 years.  Mother age = (45-3) = 42 years.

Q 7 - Ajay is as much younger to vijay as he is older to vinay. If 48 years is the sum of the ages of vijay and buwan . Then find out the present age of Mr. ajay ?

Answer - D

Explanation

V-A = A- B ⇒ V+B = 2A =48 ⇒ 24  Now,  We can say that the present age  of Mr. Ajay  is 24 years.

Q 8 - If 100 year is equal to the sum of the ages of father and son. 2:1 was the ratio of father and son before the period of 5 years. Find out the ratio of ages which would be after the period 10 year.

Answer - D

Explanation

If the age of father at the present time = x years   His son age at the present time =  (100-x) years.  x-5 / (100-x-5) = 2/1  ⇒ (x-5) = 2(95-x) ⇒ 3x = 195  ⇒ x = 65  Ratio of the ages of man and son after 10 years = (65+10)/(35+10)= 75/45 = 5/3 = 5:3

Aptitude - Squares & Cubes

Square Root

When y = x² then square root of y is x and it is written as √y = x.

For example, √9 = 3, √16 = 4 and so on.

Cube Root

When y = x³ then cube root of y is x and it is written as ∛y = x.

For example, ∛8 = 2, ∛27 = 3 and so on.

Important Formulaes

√ab = √a x √b
√(a/b) = √a / √b

Solved Examples

Q 1 - √ 2025 = ?

Answer - A

Explanation

Resolve 2025 into prime numbers first.  2025 = 5 x 5 x 3 x 3 x 3 x 3 = 5² x 3² x 3²  ∴ √2025 = 5 x 3 x 3 = 45

Q 2 - √ 54 x √ 6 = ?

Answer - C

Explanation

√ 54 x √ 6 = √ 54 x 6 = √ (3 x 3 x 6 x 6)  = √ (3² x 6²)  = √ 18

Q 3 - √(248 + √(51 + √169)) = ?

Answer - D

Explanation

√(248 + √(51 + √169)) = √(248 + √(51 + 13))  = √(248 + √(64)) = √(248 + 8) = √(256) = 16

Q 4 - √(25/16) = ?

Answer - B

Explanation

√(25/16) = √25/ √ 16 = 5/4.

Q 5 - If √15 = 3.88. What is √(5/3)?

Answer - B

Explanation

√(5/3) = (√5 / √ 3) x (√3 / √ 3) =  √15 / 3 = 3.88/ 3 = 1.293

Q 6 - If √ 1369 = 37 then what is √13.69 + √0.1369 + √ 0.001369 + √ 0.00001369?

Answer - B

Explanation

√13.69 + √0.1369 + √ 0.001369 + √ 0.00001369   = √(1369 / 100) + √(1369/ 10000) + √(1369/ 1000000) + √(1369/ 100000000)  = √1369 / √100 + √1369 / √10000 + √1369 / √1000000 + √1369 / √100000000  = 37/10 + 37/100 + 37/1000 + 37/ 10000   = 3.7 + 0.37 + 0.037 + 0.0037    = 4.1107

Q 7 - If √ 15 = 3.8729 then what is (√5 + √3)/(√5 - √3)?

Answer - A

Explanation

(√5 + √3)/(√5 - √3)   = (√5 + √3)/(√5 - √3) * (√5 + √3)/(√5 + √3)  = (√5 + √3)²/(5 - 3)  = (5 + 3 + 2√5 + √3)/2   = (8 + 2√15)/2  = 2(4 + √15)/2  = 4 + √15  = 4 + 3.8729  = 7.8729

Q 8 - ∛9261 = ?

Answer - A

Explanation

9261 = 3 x 3 x 3 x 7 x 7 x 7  = 3³ x 7³  ∴ ∛9261 = (3³ x 7³)^1/3  = 3 x 7 = 21.

Q 9 - What is the least number required to multiply to 9720 to make a perfact cube?

Answer - C

Explanation

9261 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 3 x 3  = 2³ x 3³ x 3² x 5  ∴ required no: 3 x 5² = 3 x 25 = 75

Number System - Profit & Loss

Cost Price, (c.p.) = The price, at which an article is purchased, is called its cost price.
Selling price (s.p) = The price, at which an article is sold, is called its selling price.
Profit or Gain = (S.P) - (C.P)
Loss = (C.P) - (S.P)
Gain or Loss is always reckoned on C.P.

Formulae

Gain% = (Gain*100) / C.P
Loss% = (Loss*100) / C.P
S.P = (100+ Gain %) /100 * (C.P)
S.P = (100-Loss %) / 100 * (C.P)
C.P = 100 / (100 + Gain %)* (S.P)
C.P = 100 / (100-Loss %)* (S.P)

Important cases

If an article is sold at a profit of say, 20%, then SP = 120% of CP.
If an article is sold at a loss of say, 20%, then SP = 80% of CP.
When a person sells two similar items, one at a gain of say x% and the other at a loss of say x%. then the seller always incurs a loss given by:
Loss% = (x/10)²
If a seller sells his goods at cost price but uses false weights, then
Gain% = [Error/(True value - Error) * 100]%

Solved Examples

Q 1 - A vendor bought 6 oranges for Re 10 and sold them at 4 for Re 6. Find his loss or gain percent.

Answer - D

Explanation

Suppose, number of oranges bought = LCM of 6 and 4 = 12  ∴CP = Re (10/6 * 12) = Re 20 and SP = Re (6/4 * 12) = Re 18  ∴Loss% = (2/20 * 100)% = 10%

Q 2 - By selling 33 meters of cloth, one gains the selling price of 11 meters. Find the gain percent.

Answer - A

Explanation

(SP of 33m) - (CP of 33m) = Gain = SP of 11m  ∴ SP of 22m = CP of 33m  Let CP of each meter be Re 1. Then, CP of 22m = Re 22.   Hence SP of 22m = Re 33.  ∴ %Gain = 11/22 * 100  = 50%

Q 3 - Pure ghee costs Re 100 per kg. A shopkeeper mixes vegetable oil costing Re 50 per kg and sells the mixture at Re 96 per kg, making a profit of 20%. In what ratio does he mix the pure ghee with the vegetable oil.

Answer - A

Explanation

Mean Cost price = Re (100/120)*96 = Re 80 per kg  Apply rule of allegation,    there4; Required ratio = 30:20 = 3:2

Q 4 - The CP of 25 articles is equal to SP of 20 articles. Find the loss or gain percent.

Answer - C

Explanation

Let the CP of each article = Re 1.  Then CP of 20 articles = Re 20.  SP of 20 articles = CP of 25 articles = Re 25.  ∴ Gain% = (5/20)*100% = 25%

Q 5 - A shopkeeper bought 80 kg of sugar at Re 13.50/kg and mixed it with 120 kg sugar at Re 16/kg. If he is to make a profit of 16% what rate should he sell the sugar to his customers?

Answer - D

Explanation

CP of 200 kg of mixture = Re (80 * 13.50) + (120 * 16) = Re 3000  SP = 116% of Re 3000 = Re (116/100)*3000 = Re 3480  ∴Rate of SP = Re 3480/200 = Re 17.40/kg

Q 6 - A man bought cookies at 3 for a rupee. How many for a rupee should he sell to make a profit a 50%.

Answer - B

Explanation

CP of 3 cookies = Re 1  SP of 3 cookies = 150% of Re 1 = 3/2    For Re 3/2, the man sells 3 cookies.   Hence for Re 1, number of cookies sold = 3*2/3 = 2

Q 7 - Anil buys a calculator for Re 600 and sells it to Vikash at 10% profit. Vikash sells it to Chandan for 5 % profit. Chandan after using it for certain time, sells it to Dinesh at a loss of 20%. For how much Chandan sell the calculator to Dinesh.

Answer - C

Explanation

SP for Chandan = 600 * (110/100) * (105/100) * (80/100)  = 600 * 924/1000  = Re 554.40

Q 8 - An article is sold by X to Y at a loss of 20%, Y to Z at a gain of 15%, Z to W at a loss of 5% and W to V at a profit of 10%. If v had to pay Re 500, how much X paid for it?

Answer - A

Explanation

CP for X = 500 * (100/80) * (100/115) * (100/95) * (100/110)  = 500 * 10000/9614  = Re 520.07

Q 9 - A vendor when could not find buyers for his vegetable at Re 10/kg, reduced the rate to Re 8.10 per kg but uses a faulty weight of 900 gm in place of 1 kg weight. Find the percent change in the actual price or loss.

Answer - D

Explanation

After the price was reduced, 900 gm now costs Re 8.10.  Hence 1000gm will cost (1000/900)*8.10 = Re 9  % change in actual price or loss = [(10 - 9)/10]*100%  = 10%

Q 10 - A trader marks the SP of an object at a profit of 20%. Considering the demand o the object, he further increases the price by 10%. Find the final profit %.

Answer - C

Explanation

Let the CP = Re 100  ∴ SP = 100 * (120/100) * (110/100)  = Re 132    Final profit = (132 - 100)*100%  = 32%

Q 11 - An article when sold for Re 4600 makes a 15% profit. Find the profit or loss % if it was sold for Re 3600.

Answer - C

Explanation

CP = 4600 * (100/115)  =Re 4000    Loss% = [(4000-3600)/4000]*100%  = 10%

Q 12 - A seller sells a watch at 5% loss. If he had bought it at 20% more and sold it for Re 115 less, he would have incurred a loss of 40%. Find the cost price of the watch.

Answer - A

Explanation

Assume CP = x  Selling price at the first case = (95/100)x  Selling price at the second case = (60/100)*(120/100)x  = (7200/10000)x    As per question,  (95/100)x - (7200/10000)x = 150  Or, x = Re 500

Q 13 - When a man sold an article for Re 540, he made a loss of 10%. At what price should he sell it, so that he incurs a loss of only 5%.

Answer - D

Explanation

CP = 540*(100/90)  = Re 600    New SP = 600*(95/100)  = Re 570

Q 14 - Ram sells chocolates at a profit of 20% for Re 60. What will be the percentage loss or gain if he reduces the price to Re 55 due to less demand.

Answer - C

Explanation

CP = 60*(100/120)  = Re 50  New SP = Re 55  Gain% = (5/50)*100  =10%

Q 15 - A shopkeeper buys rice for Re 1600. He had to sell 1/4th at a loss of 20%. If he is to make an overall gain of 10%, what percentage of profit he needs to make out of the remaining stock of rice?

Answer - A

Explanation

CP of 1/4th of the stock = 1600/4 = Re 400  SP of 1/4th of the stock = 400*(80/100)  =Re 320     In order to make a profit of 10% on total CP, the SP should be:  SP = 1600*(110/100)  = Re 1760    ∴The SP for the remaining 3/4th of the stock   should be Re 1760 - Re 320 = Re 1440.    Cost Price of the 3/4th of stock   = Re 1600 - Re 400 = Re 1200.  ∴%Gain = [(1440-1200)/1200*100}]  = (240/1200)*100  = 20%

Q 16 - A 10% hike in the price of wheat forces a person to purchase 2 kg less for Re 110. Find the new and the original price of the wheat.

Answer - B

Explanation

10% of Re 110 = Re 11  Cost of 2 kg of wheat at new price = Re 11  So, cost of 1 kg of wheat at new price = Re 5.50 = Re 11/2    Original Price = (11/2)*(100/110)  = Re 5 per kg

Q 17 - 10 kg of rice costs as much as 20 kg of wheat, 25 kg of wheat costs as much as 2kg of tea, 5 kg of tea costs as much as 25kg of sugar. Find the cost of 6 kg of sugar if 14 kg of rice costs Re 32.

Answer - C

Explanation

4 kg of rice costs Re 32  ∴10kg of rice will cost = (32/4)*10 = Re 80    20 kg of wheat costs Re 80.  ∴25kg of wheat costs = (80/20)*25 = Re 100    2kg of tea costs Re 100  ∴5 kg of tea costs = (100/2)*5 = Re 250    25kg of sugar costs Re 250.  ∴6 kg of sugar costs = (250/25)*6 = Re 60

Q 18 - A fruit seller sells bananas at a profit of 20%. If he increases the selling price of each banana by 25 paisa, he earns a profit of 45%. Find the initial selling price of each banana and also its cost price.

A - SP = Re1.20, CP = Re 1

B - SP = Re1.50, CP = Re 1

C - SP = Re1.20, CP = Re 1.10

D - None of the above.

Answer - A

Explanation

Let CP = x paisa.  Initial SP = x*(120/100) paisa    As per question,  120x/100 + 25 = (145/100)x  or, 145x/100 - 120x/100 = 25  or, 25x/100 = 25  or, x = 100 paisa    CP = 100 paisa or Re 1.  Initial SP = 120 paisa or Re 1.20.

Q 19 - A man sold two plots for Re 8 lakhs each. One on he earns a profit of 16% and the other he loses 16%. How much does he loss or gain in the whole transaction?

Answer - C

Explanation

Applying direct formula, %loss = (16/10)2%  = 64/25%  = 2.56%

Q 20 - An uneducated retailer marks all his goods at 50% above the cost price and thinking that he will still make 25% profit, offers a discount of 25% on the marked price. What is his actual profit on the sales?

Answer - B

Explanation

Let CP = Re 100.  The, marked price, MP = Re 150  SP = 75% of Re 150 = Re 112.50  ∴ Gain% = 12.50%

S NAGA MALLESWARA REDDY

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Aptitude - Ages

Solved Examples

Aptitude - Squares & Cubes

Square Root

Cube Root

Important Formulaes

Solved Examples

Number System - Profit & Loss

Formulae

Important cases

Solved Examples

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