SSC CGL Tier1 Quantitative Aptitude Partnership Test 2

Let the total profit be Rs. 100.

After paying to charity, As share = Rs.$ \left(95\times\dfrac{3}{5} \right) $= Rs. 57.

If As share is Rs. 57, total profit = Rs. 100.

If As share Rs. 855, total profit =$ \left(\dfrac{100}{57} \times 855\right) $= 1500.

Let C = $ x $.

Then, B = $ x $ + 5000 and A = $ x $ + 5000 + 4000 = $ x $ + 9000.

So, $ x $ + $ x $ + 5000 + $ x $ + 9000 = 50000

$\Rightarrow$ 3$ x $ = 36000

$\Rightarrow x $ = 12000

A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.

$\therefore$ As share = Rs.$ \left(35000 \times\dfrac{21}{50} \right) $= Rs. 14,700.

Let Ps capital be $p$,

Qs capital be $q$,

and Rs capital be $r$

Then

$4p=6q=10r\\2p=3q=5r \cdots(A)$

From (A),

$q=\dfrac{2p}{3}~~\cdots(1)\\r=\dfrac{2p}{5}~~\cdots(2)$

$p:q:r=p:\dfrac{2p}{3}:\dfrac{2p}{5}$

$=15:10:6$

Rs share $=4650×\dfrac{6}{31}=150×6=900$

Let the initial investments of A and B be 3$ x $ and 5$ x $.

A : B : C = $\left(3 x \times 12\right)$ :$\left (5 x \times 12\right)$ : $\left(5 x \times 6\right)$ = 36 : 60 : 30 = 6 : 10 : 5.

Arun : Kamal : Vinay = $ \left(8,000 \times 6\right)$ : $ \left(4,000 \times 8\right) $: $ \left(8,000 \times 8\right)$

= 48 : 32 : 64

= 3 : 2 : 4.

$\therefore$ Kamals share = Rs.$ \left(4005 \times\dfrac{2}{9} \right) $= Rs. 890.

Ratio in which they should share the profit

= Ratio of the investments multiplied by the time period

$=45000×12:30000×9$

$=45×12:30×9$

$=3×12:2×9$

$=2:1$

Let their investments be Rs. $ x $ for 14 months, Rs. $ y $ for 8 months and Rs. $ z $ for 7 months respectively.

Then, 14$ x $ : 8$ y $ : 7$ z $ = 5 : 7 : 8.

Now,$ \dfrac{14x}{8y} $=$ \dfrac{5}{7} $   $\Leftrightarrow $   98$ x $ = 40$ y $    $\Leftrightarrow$    $ y $ =$ \dfrac{49}{20} x $

And,$ \dfrac{14x}{7z} $=$ \dfrac{5}{8} $   $\Leftrightarrow$    112$ x $ = 35$ z $    $\Leftrightarrow$    $ z $ =$ \dfrac{112}{35} x $ =$ \dfrac{16}{5} x $.

$\therefore x $ : $ y $ : $ z $ = $ x $ :$ \dfrac{49}{20} x $:$ \dfrac{16}{5} x $= 20 : 49 : 64.

Ratio of the investment

$=21000:17500=210:175$ $=42:35=6:5$

Share of X in the profit

$=26400×\dfrac{6}{11}=2400×6=14400$

A : B =$ \left(4x \times 3 +\left(4x -\dfrac{1}{4} \times 4x\right)\times 7\right) $:$ \left(5x \times 3 +\left(5x -\dfrac{1}{5} \times 5x\right)\times 7\right) $

   = $\left(12x+ 21 x \right)$ : $\left(15 x + 28 x \right)$

   = 33$ x $ :43$ x $

   = 33 : 43.

$\therefore$ As share = Rs.$ \left(760 \times\dfrac{33}{76} \right) $= Rs. 330.

A : B : C = $\left(10 \times 7\right)$ :$\left (12 \times 5\right)$ : $\left(15 \times 3\right)$ = 70 : 60 : 45 = 14 : 12 : 9.

$\therefore$ Cs rent = Rs.$ \left(175 \times\dfrac{9}{35} \right) $= Rs. 45.