CMAT 2020

Time taken by X to reach Y's house = 25 minutes and by Y to reach X's house = 50 min

Ratio of time taken = $$1:2$$

$$\because$$ speed is inversely proportional to time, let speed of X = $$2x$$ km/min and speed of Y = $$x$$ km/min and distance between their houses = $$2d$$ km

Using, speed = distance/time

=> $$x=\frac{2d}{50}=\frac{d}{25}$$

=> $$\frac{d}{x}=25$$ -------------(i)

Now, time taken by Y to travel $$d$$ km, i.e. mid way = $$\frac{d}{x}$$

= $$25$$ minutes

Now, time taken by X to travel $$d$$ km, i.e. mid way = $$\frac{d}{2x}$$

= $$12.5$$ minutes

So, the correct answer is $$25-12.5=12.5$$ minutes

=> Ans - (D)

Principal sum to be borrower = Rs. 25,000

Amount when compounded annually = $$P(1+\frac{R}{100})^T$$

=> Amount to be paid after 3 years = $$25,000(1+\frac{3}{100})$$ $$(1+\frac{4}{100})$$ $$(1+\frac{5}{100})$$

= $$250\times103\times\frac{26}{25}\times\frac{21}{20}$$

= $$103\times13\times21=Rs.$$ $$28,119$$

=> Ans - (D)

Two successive discounts of $$x$$ and $$y$$ $$\equiv x+y-\frac{xy}{100}$$

= $$12+8-\frac{12\times8}{100}$$

= $$20-0.96=19.04\%$$

=> Ans - (B)

Let cost price of each article = Rs. 100 and number of articles sold be $$x$$

=> Original selling price price = Rs. 125

=> Original profit = Rs. $$(125-100)x = Rs.$$ $$25x$$

After offering discount of 8%, => New selling price = $$\frac{92}{100}\times125=Rs.$$ $$115$$

Also, new cost price = $$\frac{95}{100}\times100=Rs.$$ $$95$$

$$\because$$ Sale increases by 25%, => Number of articles now sold = $$1.25x$$

=> New profit = Rs. $$(115-95)\times1.25x = Rs.$$ $$25x$$

$$\therefore$$ There is no change in profit.

=> Ans - (A)

Probability of brother's selection = $$\frac{1}{8}$$ and probability of brother's rejection = $$\frac{7}{8}$$

Probability of sister's selection = $$\frac{1}{5}$$ and probability of sister's rejection = $$\frac{4}{5}$$

Probability that only one of them is selected = (prob. that brother is selected) × (prob. that sister is not selected) + (Prob. that brother is not selected) × (Prob. that sister is selected)

= $$(\frac{1}{8})(\frac{4}{5})+(\frac{7}{8})(\frac{1}{5})$$

= $$\frac{4}{40}+\frac{7}{40}=\frac{11}{40}$$

=> Ans - (A)

Let Steve's salary = $$Rs.$$ $$10$$

=> John's salary = $$\frac{80}{100}\times10=Rs.$$ $$8$$

=> Tom's salary = $$\frac{150}{100}\times8=Rs.$$ $$12$$

$$\therefore$$ Ratio of Steve's salary to Tom’s salary = $$\frac{10}{12}=5:6$$

=> Ans - (D)

There are 2 physics teacher.They can stand in a row in $$P(2,2)=2!=2\times1=2$$ ways

Similarly, the two Chemistry and Mathematics teacher can stand in 2 ways each.

These three sets can be arranged in themselves in $$3!=3\times2\times1=6$$ ways

=> Required number of ways = $$2\times2\times2\times6=48$$

=> Ans - (B)

Sum of ages of A, B, C and D five years ago = $$45\times4=180$$

Sum of their present ages = $$180+(5\times4)=200$$

Sum of present ages of all five (including X) = $$49\times5=245$$

=> Present age of X = $$245-200=45$$ years

=> Ans - (B)

In a triangle, the sum of two sides is always greater than the third side.

In the last two options, sum of first two sides is less than third side, and in first two options sum is equal to third side, hence these three are not possible.

Thus, possible lengths of triangle = [5,7,9]

=> Ans - (B)

Taking the vowels (EA) as one letter, the given word has the letters XTR (EA), i.e., 4 letters.

These letters can be arranged in $$4! = 24$$ ways

The letters EA may be arranged amongst themselves in $$2!=2$$ ways.

Number of arrangements having vowels together = $$(24 \times 2) = 48$$ ways

Total arrangements of all letters = $$5!=120$$ ways

=> Number of arrangements not having vowels together = $$(120 - 48) = 72$$ ways

=> Ans - (D)