Quantitative Aptitude Prep Tips for MBA

Let the CP of apple be p

Then, px + (p + 4)y – 8 = p * 3x + (p+4) (y–6)

px +py +4y = 3px + py – 6p + 4y – 24 + 8

2px – 6p = 16

p (x–3) = 8

The maximum value of p is 8 at x = 4

Then, CP of an apple and mango is 8 + 12 = 20 Rs.

Let fare for business class and economy class be Rs. 3x and Rs. 2x respectively. Let the passenger in business class and economy class be 12y and 25y respectively.

Total fare = 3x * 12y + 2x * 25y

=86xy = 430000

xy = 5000

Absolute difference = (50 – 36) * 5000

= Rs.70, 000

Let X = Total Amount of Gold

& Y = Total Amount of Platinum

$\frac{}{}$ $\frac{X}{Y}=\frac{2}{5}$  . (1)

Given U1 + P1 = U2 + P2. (2)

U1 + U1 = X & P1 + P2 = Y. (3)

Also, given U1 = 3U2

From (2) P2 − P1 = 2U2

Also, X = 4U2 & 2P1 = Y − 2U2

$\frac{X}{Y}=\frac{2}{5}=\frac{4U_2}{2P_1+2U_2}$

4P1 + 4U2 = 20U2

4P1 = 16U2 $=\frac{16}{3}{U}_1$

$\frac{U_1}{P_1}=\frac{4*3}{16}=\frac{3}{4}$ $\frac{}{}{}_{}$

U1 : P1 = 3 : 4

Let Gopal's share be G, Abhishek's be A, Sadiq's be S and Pawan's be P.

Given that $G+3=A+\frac{A}{3}=\frac{80S}{100}=P-4$ $\frac{}{}\frac{}{}$

You get

G = P – 7. (1)

$$ $A=\frac{3}{4}(P-4)$  . (2)

$$ $S=\frac{5}{4}(P-4)$  …. (3)

Also given that G + A + P + S = 80…. (4)

Substituting the values from (1), (2) and (3) in (4), we get

$\frac{}{}\frac{}{}$  $\left[P+\frac{3P}{4}+\frac{5P}{4}+P\right]-7-3-5=80$ or P = 23.75

For n = 14, 39 (1 + 33 + 36 + 35)

= 39 (1 + 27 + 729 + 243)

= 39 * 103.

Volume of tube $=\frac{2}{3}\pi a^3+\pi a^{2}b$ $\frac{}{}{}^{}{}^{}$

When it is half-full $=\frac{1}{3}\pi a^3+\frac{1}{2}\pi a^{2}b$ $\frac{}{}{}^{}\frac{}{}{}^{}$

Volume of Cylinder

$=\frac{1}{3}\pi a^3+\frac{1}{2}\pi a^{2}b-\frac{2}{3}\pi a^3=\frac{1}{2}\pi a^{2}b-\frac{1}{3}\pi a^3$

Length in the cylinder

$=\left(\frac{1}{2}\pi a^{2}b-\frac{1}{3}\pi a^3\right)÷\pi a^2=\frac{1}{2}b-\frac{1}{3}a$

The height above the lowest point

$\frac{1}{2}b-\frac{1}{3}a+a=\frac{2}{3}a+\frac{1}{2}b$

When it is $\frac{1}{4}$ $\frac{}{}$ full, volume $=\frac{1}{6}\pi a^3+\frac{1}{4}{\pi }^{a}b$ $\frac{}{}{}^{}\frac{}{}{}^{}$

Volume of cylinder

$=\frac{1}{6}\pi a^3+\frac{1}{4}\pi a^{2}b-\frac{2}{3}\pi a^3=\frac{1}{4}\pi a^{2}b-\frac{1}{2}\pi a^3$

Length in the cylinder

$=\left(\frac{1}{4}\pi a^{2}b-\frac{1}{2}\pi a^3\right)÷\pi a^2=\frac{1}{4}b-\frac{1}{2}a$

The height above the lowest point

$=\frac{1}{4}b-\frac{1}{2}a+a=\frac{1}{2}a+\frac{1}{4}b$

When it is full, volume 

$=\frac{3}{4}\left(\frac{2}{3}\pi a^3+\pi a^{2}b\right)=\frac{1}{2}\pi a^3+\frac{3}{4}\pi a^{2}b$

Volume in cylinder

$=\frac{1}{2}\pi a^2+\frac{3}{4}\pi a^{2}b-\frac{2}{3}\pi a^3=\frac{3}{4}\pi a^{2}b-\frac{1}{6}\pi a^3$

Length in the cylinder

$=\left(\frac{3}{4}\pi a^{2}b-\frac{1}{6}\pi a^3\right)÷\pi a^2=\frac{3}{4}b-\frac{1}{6}a$

The height above the lowest point

$=\frac{3}{4}b-\frac{1}{6}a+a=\frac{5}{6}a+\frac{3}{4}b$

The average age of n men is X year. Total age is given by N years

$\begin{array}{l}Newaverageage =\frac{NX+X-1+X+1+X+2}{N+3}\\ =\frac{NX+3X+2}{N+3}\\ =\frac{X[N+3]}{N+3}+\frac{2}{N+3}\\ \Rightarrow X+\frac{2}{N+3}\end{array}$

Total time = 182s

2 + 4 + 6 + 8 +……………+ n terms = 182

i.e. n=13

Total distance covered = 2* [1² + 2 ²+ 3² +……. …………. + 13²]

= 2 * 13 * 14 * $\frac{27}{6}$  = 9 * 13 * 14m

Average speed = 9 * 13 * $\frac{4}{182}$ = 9m/s

The bag has 25-paise, 50-paise and 1 -rupee coins in the ratio 8 : 2 : 7. Now this is the ratio of the number of coins while the total value of the coins has been given. So we first need to convert coins into value.

Let the coins be 8x, 2x and 7x respectively.

8x coins of 1/4 rupee each = value is Rs. 2x.

2x coins of 1/2 rupee each = value is Rs. x.

7x coins of 1 rupee each = value is Rs. 7x.

Now

2x + x + 7x = 770

10x = 770 x = 77

Number of 25 paise and 50 coins = 10 x = 770 coins

Let daily working hours & wages per hour before increase be H and W respectively

So his Salary/day = HW

Working hours after increase = 0.82H, wages per hour = 1.45W

So his daily salary = $\frac{82}{100}H*\frac{29}{20}W=\frac{1189}{1000}HW$ $\frac{}{}\frac{}{}\frac{}{}$ . Thus an Increase of 18.9%