CAT Questions

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LCM of 2, 3, 7 is 42.

=> (700 – 300)/42 = 9  22/42 => 9 Numbers.

Let the present ages of Ajay and Vijay be 'A' and 'V' years respectively.

=> A - 8 = 4/3 (V - 8) and A + 8 = 6/5 (V + 8)

=> 3/4(A - 8) = V - 8 and 5/6(A + 8) = V + 8

V = 3/4 (A - 8) + 8 = 5/6 (A + 8) - 8

=> 3/4 A - 6 + 8 = 5/6 A + 20/3 - 8

=> 10 - 20/3 = 10/12 A - 9/12 A

=> 10/3 = A/12 => A = 40.

Let 'd' be the distance and 's' be the speed and 't' be the time
d=sxt
45 mins = 3/4 hr and 48 mins = 4/5 hr
As distance is same in both cases;
s(3/4) = (s-5)(4/5)
3s/4 = (4s-20)/5
15s = 16s-80
s = 80 km.
=> d = 80 x 3/4 = 60 kms.

The first lost Rs. 100, but after the thief bought Rs. 60 goods, he get that Rs. 100 back but he lost Rs. 60 value of goods and Rs. 40 in change.

So, a total of 60 + 40 = 100 Rs. the owner lose.

From the given data,

=> (2 M + 3W) 8 = (3M + 2W)7

=> 16M + 24W = 21M + 14 W

=> 10W = 5M

=> 2W = M

=> 14W × ? = 7W × 8

? = 4 days

Let the mother's present age be x years.

Then, the person's present age = 2/5 x years.

(2x/5 + 8) = 1/2 (x + 8)

2(2x + 40) = 5(x + 8) => x = 40.

The CP of profitable cow  = 9900/1.1 = 9000

and profit = Rs. 900

The  CP of loss yielding cow = 9900/0.8 = 12375

and loss = Rs. 2475

so, the net loss = 2475 - 900 = 1575

Speed in upstream = Distance / Time = 3 x 60/20 = 9 km/hr.

Speed in downstream = 3 x 60/18 = 10 km/hr

Rate of current = (10-9)/2 = 1/2 km/hr.