AP ICET 26th April 2019 Shift-1

Let the number is x

Now, as per the condition given in the question,

$$\Rightarrow \dfrac{40x}{100}+84=x$$

$$\Rightarrow 0.4x+84=x$$

$$\Rightarrow x-0.4x=84$$

$$\Rightarrow 0.6x=84$$

$$\Rightarrow x=\dfrac{84}{0.6}=\dfrac{840}{6}=140$$

$$x=140$$

As per the given question,

The cost price of one book $$=\dfrac{100}{11}$$

The sale price of one book $$=\dfrac{110}{10}$$

Hence the required percentage $$=\dfrac{(11-9.09)\times 100}{9.09}$$

$$=\dfrac{1.91\times 100}{9.09}=21% Profit$$

The partnership ratio of P and Q $$=9:7$$

As per the question, at the end of the 8 months, Q withdraw his amount,

The ratio in the profit is given as 9:4

So, we know that profit sharing ratio $$=\dfrac{C_P\times T_P}{C_Q\times T_Q}$$

$$\Rightarrow \dfrac{9}{4}=\dfrac{9\times T_P}{7\times 8}$$

$$\Rightarrow \dfrac{9}{4}=\dfrac{9\times T_P}{56}$$

$$T_P=\dfrac{56}{4}=14$$

as in the given question,

total profit$$=55000$$

shared profit of P,Q,R will be$$=x+4x+5x$$

then,sum of profit will be$$\Rightarrow x+4x+5x=55000$$

$$x=5500$$

then,the profit of $$P=1\times 5500$$

profit of Q $$=4\times 5500=22000$$

difference of profit between Q and P=Profit of Q-Profit of P

$$\Rightarrow 22000-5500=16500$$

So the difference of profit between Q and P is 16500

Part filled without leak in 1 hour $$= \dfrac{1}{9}$$
Part filled with leak in 1 hour $$=\dfrac{1}{10}$$

Work done by leak in 1 hour$$=\dfrac {1}{9}-\dfrac{1}{10}=\dfrac{1}{90}$$

We used subtraction as it is getting empty.

So total time to empty the cistern is 90 hours

Car A starts at 8AM with the speed of $$65kmph$$

Car B starts at 9AM with the speed of $$70kmph$$

Both starts from the point P,

Let after the time t, both the car will meet.

$$d=65\times t---------(i)$$

$$d=70\times (t-1)-------(ii)$$

From the equation (i) and (ii)

$$65\times t=70\times t-70$$

$$5\times t=70$$

Hence t=14 hour.

Hence both the car will meet 10PM

Let P will complete the work in 15 days

P can do the work in one day $$=\dfrac{1}{15}$$

Q can finish the work in 20 days.

Q can do the work in one day $$\dfrac{1}{20}$$

Let R can do the work in x days.

R can do the work in one day $$\dfrac{1}{x}$$

If P, Q and R working together, then they can finish the work in 5 days.

Hence, working together, then can do the work in one day $$\dfrac{1}{15}+\dfrac{1}{20}+\dfrac{1}{x}=\dfrac{1}{5}$$

$$\Rightarrow \dfrac{1}{x}=\dfrac{1}{5}-\dfrac{1}{15}-\dfrac{1}{20}$$

$$\Rightarrow \dfrac{1}{x}=\dfrac{1}{5}-\dfrac{7}{60}$$

$$\Rightarrow \dfrac{1}{x}=\dfrac{5}{60}=\dfrac{1}{12}$$

Hence x=12 days. So , R can finish the work in 12 days.