Quantitative Aptitude - Arithmetic Ability Questions

Given that train K crosses a pole in 30 seconds and train L crosses the same pole in one minute and 15 seconds.

Let the length of train K be Lk and that of train L be Ll

given that Lk = 3/4 Ll

As the train K and L crosses the pole in 30 seconds and 80 seconds respectively,
=> Speed of train K = sk = Lk/30

Speed of train L = sl = Ll/80

Lk = 3/4 Ll
=> sk = 3/4 Ll/(30) = Ll/40

Ratio of their speeds = sk : sl
= Ll/40 : Ll/80

=> 1/40 : 1/80  =  2 : 1

Let Althaf lent Rs. A at 14% per year.
Hence, Money lent at 12% = (1500-A);
Given, total interest = Rs. 186.
{(A x 14x 1)/100} + {[(1500-A) x 12 x 1/100]} = 186;
14A/100 + (18000 -12A)/100 = 186;
14A + 18000 - 12A = 186x100;
2A = 18600-18000;
A = 600/2 = Rs. 300.
Hence, money lent at 12% = 1500-300 = Rs. 1200.

Let t be the usual time. If the usual rate is 1 unit, then the unusual rate is 6/7.
Balance by the distance,
1 x t = (6/7)(t + 30)
7t = 6(t + 30)
we get t as,
t = 180 minutes = 3 hrs.

In the given series 1 4 9 16 22 36

1 = 1 x 1 

4 = 2 x 2

9 = 3 x 3

16 = 4 x 4

25 = 5 x 5 (Not 22)

36 = 6 x 6

Hence, the odd man in the series is 22.

Given:j=7% compounded semiannually making m=2 and i = j/m= 7%/2 = 3.5%
Let x represent the third payment. Then the second payment must be 2x.
PV1,PV2, andPV3 represent the present values of the first, second, and third payments.

Since the sum of the present values of all payments equals the original loan, then
PV1 + PV2  +PV3
=$4000 -------(1)

PV1
  =FV/(1 + i)^n
=$1000/(1.035)^4=
$871.44

At first, we may be stumped as to how to proceed for
PV2 and PV3. Let’s think about the third payment of x dollars. We can compute the present value of just $1 from the x dollars

pv=1/(1.035)^10=0.7089188

PV2
  =2x * 0.7089188 =
1.6270013x
PV3
  =x * 0.7089188=0.7089188x
Now substitute these values into equation ➀ and solve for x.
$871.442 + 1.6270013x + 0.7089188x
=$4000

2.3359201x
=$3128.558

x=$1339.326
Kramer’s second payment will be 2($1339.326)
=$2678.65, and the third payment will be $1339.33

Compound Interest for 1 ¹⁄₂ years when interest is compounded yearly = Rs.(5304 - 5000)

Amount after 1¹⁄₂ years when interest is compounded half-yearly 


Compound Interest for 1 ¹⁄₂ years when interest is compounded half-yearly = Rs.(5306.04 - 5000)

Difference in the compound interests = (5306.04 - 5000) - (5304 - 5000)= 5306.04 - 5304 = Rs. 2.04

let speed of boat= X, speed of stream= Y
Upstream speed= X-Y
Downstream speed= X+Y
Sum of upstream & downstream= (X-Y) +(X+Y)= 2X
So, 2X= 40
X= 20 km/hr
Speed of boat : speed of stream= 600+100 :100= 7:1
So speed of Stream= 20/7 km/hr
ATQ, D/( X-Y) + D/( X+Y) = 5
D/(120/7) + D/(160/7)= 5
D= 480×5/49= 48.97 km= 50 Km(approx)

we know that speed = distance traveled/time taken
let the total distance traveled by the car is 2x km.
then time taken by it to cover first half is x/60 hour.
and for second half is x/40 hour.
Then average speed= total distance travelled / total time taken.

i.e. 2xx60+x40

=> 2x5x120

= 48 kmph.