## Aptitude (Case Studies New pattern questions) day 17

Directions.1-5) Study the following passage and answer the questions accordingly.

Five trains A, B, C, D and E of lengths  250m, 500m, 750m, 1000m, 1250m reach their destination in 5 h, 10 h, 15 h, 20 h and 25 h respectively. Those trains A, B, C, D and E are running at 20km/h, 40km/h, 60km/h, 80km/h and 100km/h.

Q.1) If A and C are moving in the same direction at their respective speeds. Find the time taken by the faster train to cross the slower train.

a) 45 s

b) 90 s

c) 54 s

d) 72 s

e) None of these

Total lengths of Train A and C=250+750=1000m=1km

Relative speed in case of the trains moving in same direction= S1-S2

=60-20=40kmph

Time required to cross each other=Distance/Time=1/40=0.025hrs=90s

Q.2) If Train E is running at ‘x’ km/hr. In what time, will it pass a man running at 10 km/h in the same direction in which the train is going?

a) 48 s

b) 45 s

c) 50 s

d) 66 s

e) None of these

Speed of the train relative to man=100-10=90km/h

=90×5/18=5×5=25 m/s

Distance covered in passing the man=1250 m

Time taken=1250/25=50 s

Q.3) Train B passes a platform of length 350m in 50s. What time will this train take to pass the platform of 230 m length?

a) 35 s

b) 16 s

c) 27 s

d) 43 s

e) None of these

Length of train B=500m;   Length of platform=350m

Time taken to cover the distance=50 s

So, to cross the platform, the train has to cover a distance

=Length of train+Length of platform=500+350=850m

Speed of train=(Distance covered)/(Time taken)=850/50=17m/s

Time taken to cover the platform of length 230m=(500+230)/17=730/17=43 s

Q.4) If from stations P and Q, two trains C and D start moving towards each other with their respective speeds. When the two trains meet each other, it is found that one train covers 20 km more than that of another train. Find the distance between stations P and Q.

a) 140 km

b) 130 km

c) 120 km

d) 110 km

e) None of these

Here, Speed of C=60km/h;   speed of D=80 km/h and  distance=20 km

According to the formula,

Distance between stations P and Q=(D+C)/(D-C)×distance

=(80+60)/(80-60)×20=140 km

Q.5)Two trains B and C leave from their stations X and Y at 10:00am and 10:30am respectively and travel at 40 km/h and 60 km/h, respectively. How many kilometers from X, will the two trains meet?

a) 50 km

b) 60 km

c) 70 km

d) 80 km

e) None of these

Here, B=40km/h;C=60km/h;    t1=10:00am and t2=10:30am

According to the formula,

Required distance=(t2-t1)×(B×C)/(C-B)=(10:30-10:00)×(40×60)/(60-40)

=1/2×2400/20=60km

A person invests some amount in scheme A which offers 5% interest compounded annually. At the same time, he accrues a simple interest of Rs.220 in scheme B such that the money invested in scheme B is 9900 lesser than that invested in the scheme A two years before.

He lends money privately to a tea shop who repays the money in a single installment. He withdraws the money invested in the scheme A after 2 years and lends it to the tea shop owner at 10% simple interest. The ratio of the money invested by him in scheme A and scheme B is 10:1.

Q.6) What is the interest acquired by the person in scheme A (in Rs.)?

a) 1645.5

b) 2244.5

c) 983.5

d) 1127.5

e) None of these

Here, the difference between the sum invested in scheme A and scheme B is=9900

The ratio between the sum invested in scheme A and scheme B=10:1

The sum invested in scheme A =11000 Rs.

The rate of interest= 5%

The number of years for which he invested=2

The amount accrued at the end of 2 years 11000(1+5/100)2  = Rs.12127.5

The interest accrued= 12127.5-11000= Rs. 1127.5.

Q.7) How much money should the tea shop owner give at the end of 4 years?

a) 4851

b) 16978.5

c) 21829.5

d) 9702

e) None of these

The sum lent to him= The amount obtained in scheme A= Rs.12127.5

The interest to be given =(12127.5×4×10)/100= Rs.4851

Q.8) What is the average of interest acquired in all the investments?

a) 3122

b) 1879

c) 2702

d) 2066

e) none of these

The interest accrued in scheme A= 1127.5

The interest accrued in scheme B=220

The interest accrued from tea shop=4851

The average of interest money acquired =(1127.5+220+4851)/3=2066

Q.9) The interest money acquired in scheme B is what percent of the interest acquired from the tea shop owner?

a) 6.4%

b) 7.1%

c) 3.9%

d) 5.7%

e) 4.5%

The interest acquired in scheme B= 220

The interest acquired from tea shop= 4851

Required % =220/4851×100=4.5%

Q.10) What is the ratio of the sum of money invested in scheme A and the interest acquired from scheme A together to the interest acquired in scheme A and the money invested in scheme B together?

a) 99:341

b) 539:99

c) 101:539

d) 341:101

e) 99:101

The sum of money invested in scheme A and the interest acquired from scheme A =11000+1127.5=12127.5 Rs

The interest acquired in scheme A and the money invested in scheme B

=1127.5+1100=2227.5

Required ratio =12127.5:2227.5 =539:99