Maths

Let A (4, 3), B (6, −2), C (−11, −3) be the vertices of triangle ABC.

AB² = (6 – 4)² + (−2 −3)² = 29

BC² = (−11 −6)² + [−3 – (−2)]² = 290

AC² = (−11 −4)² + [ (−3 −3)]² = 261

As AB²+ AC²= BC²

 ABC is a right-angled triangle.

Slope of given line = $-\frac{2}{3}$ perpendicular line has slope = $\frac{2}{3}$

Now c = −3 (given)

Putting in general equation y = mx + c

2y = 3x ⇒ 3x-2y=6

Total expenses = (35% of 7500) + 712 + 1880 + 272 + 400 + 75 = 6024

Total receipts = 7500 Total profit = 7500 – 6024 = 1476

% profit = $\left(\frac{1476}{6024}\right)*100=24.5\mathrm{\%}$

We can see that men, women & children are in the ratio = $\frac{12}{6},\frac{15}{5},\frac{16}{4},$ or 2: 3: 4.Number of men, women & children = 10, 15, 20. Now if each man gets 6a, we have10 * 6a + 15 * 5a + 20 * 4a = 1720 or a = 8. So, the answers are Rs. 48, 40, 32.

Only possibility is if 1950 is divided by a multiple of 13, because the other glasses have a capacity that is not a multiple of 13.

Hence 1209 is the only choice.

Alternative method:

As the glasses filled by same fractions,

$\frac{a}{750}=\frac{b}{1950}=\frac{c}{600}=\frac{a+b+c}{750+1950+600}$

a + b + c = 2046 $\therefore \frac{b}{1950}=\frac{2046}{3300}$

b = 1209 litres

Let the number of men be x

$\frac{4x}{3(95-x)}=\frac{8}{9}$

9 x = 570 – 6 x

x = 38, so number of men is 38

$\frac{T1speed}{T2speed}=\sqrt[]{\frac{TimetakenbyT2toreachChennai}{TimetakenbyT1toreachYeshvantpur}}$

$or\frac{45}{T2speed}=\sqrt[]{\frac{200}{242}}=\frac{10}{11}$

T2 speed = $\frac{99}{2}$ $\frac{}{}$ =49.5 km/hr.

As per the problem, we have CP of 18? SP of 18 = CP of 3

CP of 15 = SP of 18

But CP of 15 toffees = Rs. 90

So SP of 18 toffees = Rs. 90

SP per toffee $=\frac{90}{18}=Rs.\text{?}5$

Let 100 units be B's income and X units be B's expenditure A's income = 60 units

A's expenditure =   $\frac{50X}{100}unitsBut60=\left(\frac{80}{100}\right)*X\Rightarrow X=75$ $$

B's saving = (100 – 75) units = 25 units

Hence, A's saving = 

60 − $\left(\frac{50}{100}\right)*75units=22.5units$ $$

A's saving : B's saving = 22.5 : 25 = 9 : 10

f CP = 100, MP = (100 + 44) * $\frac{100}{90}$ $\frac{}{}$ = 160

If MP = 23200, CP = 23200 * $\frac{100}{160}$ $\frac{}{}$ = 14500