Deloitte aptitude questions

• Even numbers between 50 and 150 is 52,54,.....,148.

• Average = \(\frac{52+148}{2}\)

• Average = \(\frac{200}{2}\) = 100

  = \(\frac{200}{2}\) = 100.

• Let MP = 100 rs , Discount = 10% , then SP = 90 rs

  Gain = 20% \(\Rightarrow\) 120% = 90

  Let 100% = \(x\)

  = 20% \(\Rightarrow\) 120% = 90

  \(\Rightarrow\) 120% = 90

  \(\Rightarrow\) 100% = \(x\)

• Do Cross multiply

  = \(\frac{90\times100}{120}\) = 75

  or

  \(x\times120 = 90\times100\)

  \(x\) = 75 \(x\times120 = 90\times100\)

  \(x\) = 75

  ie, CP = 75

  If discount = 20% , SP = 80

• Profit = \(\frac{SP - CP}{CP}\times100\)

  = \(\frac{5}{75}\times100\)

  = \(\frac{20}{3}\)%.

• Average of first 140 odd numbers = 140,

• ie, the same number itself.

• Answer is 140.

• Loss = CP - SP = 1800 - 1500 = 300

• Loss % = \(\frac{loss}{CP}\times 100\)

  = \(\frac{300}{1800}\times 100\)

  = \(\frac{100}{6}\)

  = 16.66%.

• \(A \rightarrow \)125, \(B\rightarrow 100\)

  B's salary is 25 rupees less than A's salary.

  \(\frac{25}{125}\times100=20\)% less.

• Easy Method :

  Take B's salary as 100

  Then the salary of A is 125

• In such questions, first write as follows

  

  B's salary is 25 rupees less than A's salary.

• Divide the difference 25 by the non-100 number 125. Then multiply by 100

  \(\frac{25}{125}\times100=20\)% less.

• The average speed is the total distance traveled by the object in a particular time interval.
• Average speed =\(\frac{2ab}{a+b}\)=\(\frac{2\times45\times30}{45+30}=\frac{2700}{75}=36\)km/h
• Answer is 36 km/hr

• Here, P = \(3000\)
  T = \(2\) years
  R = \(6\) %
• SI = \(\frac{PRT}{ 100}\)
  SI = \(\frac{3000 \times 2 \times 6}{100}\)
  SI = \(360\) rs
  Here, in this question Amount is asked
• Amount = P + SI
  Amount = \(3000 + 360 = 3360\) rs

• We know that,

  \(\sqrt{x\sqrt{x\sqrt{x.......}}}\) =x

• Therefore,

\(\sqrt{15\sqrt{15\sqrt{15.......}}}\) = 15

• Answer is 15

• We know that,

  \(\sqrt{x\sqrt{x\sqrt{x.......}}}\) = x

• \(\sqrt{20\sqrt{20\sqrt{20.......}}}\) =20

• Answer is 20

• Distance=\(\frac{s_{1}\times s_{2}}{s_{1}- s_{2}}\times t_{1}- t_{2}\)

• Convert time into hour

  =\(\frac{8\times6}{2}\times \frac{12-(-28)}{60}\)

  =\(\frac{8\times6}{2}\times \frac{40}{60}\)

  =16 km

• Answer is 16 km.

• Ratio of Suman's and Sumati's 1 day's work \(=\)

  \(\frac{1}{3}: \frac{1}{2}=2: 3\)

• Sum of the ratios \(=2+3=5\)

• Suman's share \(=\frac{2}{5} \times 150=Rs. 60\)

• Total age of father and mother =\( 38×2= 76 \)

• Total age of father, mother and daughter =\( 28×3= 84 \)

• Therefore age of daughter =\( 84−76= 8 \)

• We know that speed in the still water = \( \frac{a+b}{2} \)

  here a = 11kmph, b = 5kmph

• speed of the boat is still water = \( \frac{11+5}{2} \)= 8kmph

• Answer is 8kmph

• Here Man's rate in the still water= (35-12.5)\( \frac{Km}{hr} \)

• Man's rate against the current will be=( 12.5-12.5)=0\( \frac{km}{hr} \)
• Answer is 0 km.

• Given, ratio of angles of a triangle = 2 : 3 : 5.
• Sum of all three angles of a triangle is 180°.
• Ratio of angles of a triangle = 2x : 3x : 5x

• According to the question

  2x + 3x + 5x = 180°

  ⇒ 10x = 180°

  ⇒ x = 18°

• Smallest angle is = 2 × 18° = 36°

• Greatest angle is = 5 × 18° = 90°

• ∴ Required ratio = 90° : 36° = 5 : 2

Calculation :

• Time taken by A to finish the work \(=40\) days

  Time taken by B to finish the work \(=60\) days

• Total time taken \(=\frac{x \times y}{x+y}\) days

  \(=\frac{40 \times 60}{40+60}\)

  \(=\frac{40 \times 60}{100}=24\) days

Hence the answer is option C

• When numerators are small and denomenators are big and difference between numerator and denomenator is same ,we can find the highest value by pick the one which have highest numeartor.

• In this question \(\frac{20}{22}\) is the highest fraction.

• It can also find by using division method.

• If we take the number as \(x \), then half of the number is \(\frac{x}{2}\) <br>

  \( x \times \frac{39}{100} + 88\) = \(\frac{x}{2} \)

  \( \frac{39x}{100} + 88\) = \(\frac{x}{2} \)

  \(\frac{x}{2} \) - \( \frac{39x}{100}\) = 88

  \(\frac{50x-39x}{100} \) = 88

  \(\frac{x \times11}{100} \) = 88

  That is, 11% of x is 88 <br>

• 11% \( \rightarrow\) 88 <br> 20 % \(\rightarrow\)?

• 20% of the number = <br>

  \(\frac{88\times 20}{11} \)= 160

Easy Method :

• Suppose the number is \( x \).

  Adding 39% of \( x \) to 88 gives half of that number.

  That is, half of \( x \) gets \( \Rightarrow\) 50% of \( x \)

  39% + 88 = 50% of \( x \)

  \( \Rightarrow\) 88 = 11%

  11% \( \rightarrow\) 88 <br> 20 % \(\rightarrow\)?

• To find 20% of the number, just multiply them crosswise and divide them as shown below.

  

• 20% of the number \( \Rightarrow\) \(\frac{88\times 20}{11} \)= 160

• According to BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition, and at the end Subtraction.

• \((10\times15-15)\div(3.2+5.8)-7=(150-15)\div9-7\)

  \(=135\div9-7=15-7=8\)

• Answer is 8.

• Ratio = 11x : 6x

  Five years ago (11x - 5) = 2(6x -5)

  11x - 5 = 12x - 10

  x = 5

  So, the age of mom = 55 and age of son = 30

• From 20 years, mom = 75 and son = 50

  So, Son's age will the Mother's age be twenty years from now will be 1.5 times

• Answer is 1.5 times.