Quantitative Aptitude for SBI Exam 2018: 24 April
Directions (Q. 12) : Rani is going to cover a distance of 360 km from Fatehpur to Barabanki. The first one third of the distance she covers on a twowheeler. The second one third distance she covers by a threewheeler and the remaining distance by the fourwheeler. The average speed of the journey by the fourwheeler is 5 times the average by the twowheeler and 20 km/hr more than the average speed by the threewheeler, but she took 1 hour more by the threewheeler, than by the fourwheeler.
1 What is the time taken in the whole journey?
1: 18 hrs
2: 16 hrs
3: 15 hrs
4: 12 hrs
5: 24 hrs
2 What is the average speed of the whole journey?
1: 18 km/hr
2: 24 km/hr
3: 30 km/hr
4: 20 km/hr
5: 16 km/hr
1: 18 km/hr
2: 24 km/hr
3: 30 km/hr
4: 20 km/hr
5: 16 km/hr
3. The simple interest obtained when a certain sum of money is invested in scheme M for 2 yrears is Rs. 23.76 lessthan the simple interest obtained when the same sum of money is invested in scheme N for 3 years . If the rates of interest offered by Scheme M and Scheme N are 15% p.a. and 12% p.a. respectively, how much money was invested in these schemes individually?
1: Rs. 420
2: Rs. 396
3: Rs. 360
4: Rs. 482
5: Rs. 375
4. Two trains A and B start from two stations X and Y towards each other. After passing each other they take 9 hours and 4 hours to reach station Y and station X respectively. If the speed of train A is 54 kmh–1 then what is the speed of train B?
1: 48 kmh^{–1}
2: 36 kmh^{–1}
3: 64 kmh^{–1}
4: 72 kmh^{–1}
5: 81 kmh^{–1}
5. A circular path runs round a circular garden. If the difference between the circuference of the outer circle and inner circle is 132m. Find the width of Path?
1: 16m
2: 24m
3: 14m
4: 21 m
5: 12m
6. A mixture contains wine and water in the ratio 3 : 2 and another mixture contains them in the ratio 4 : 5. How many litres of the latter must be mixed with 4 litres of the former so that the resultant mixture may contain equal quantities of wine and water ?
1: 13/5 litre
2: 7/4 litre
3: 18/5 litre
4: 36/5 litre
5: None of these
7. A contractor undertook to complete a project in 90 days and employed 60 men on it. After 60 days he found that ^{3}/_{4} of the work has already been completed. How many men can he discharge so that the project may be completed exactly on time?
1: 20
2: 25
3: 45
4: 30
5: None of these
8. The average age of mother, father and son was 42 yrs. at the time of the marriage of the son. After one year and infant was born in the family and after 6 yrs of marriage the average age of the family is 36 yrs. What was the age of the bride at the time of marriage.
1: 20 yrs
2: 25 yrs
3: 30 yrs
4: 28 yrs
5: None of these
8. From a group of 3 men, 4 women and 2 children, 4 people are to be chosen to from a committee. What is the probability that the committee contains at least one men, one women and one children?
1: 4/13
2: 11/27
3: 4/7
4: 7/15
5: None of these
9. A man can cross a downstream river by steamer in 40 minutes and same by boat in 60 minutes. If the time of crossing the river in upstream direction by steamer is 50% more than downstream time by the steamer and the time required by boat to cross the same river by boat in upstream is 50% more than the time required in downstream by boat. What is the time taken by the man to cross the river downstream by steamer and then return to same place by boat half the way and by steamer the rest of the way?
1: 90 min
2: 136 min
3: 145 min
4: 75 min
5: 115 min
Answers:
 Two Wheeler Three Wheeler Four wheelerSpeed x (5x–20) 5xTime (t +1) tDistance 120km 120km 120km
⇒ x2 – 4x – 96 = 0
∴ x = 12
Time taken by two wheeler = 120/12 = 10 hrs
Time taken by three wheeler = 120/40 = 3hrs
Time taken by four wheeler = 12/60 = 2 hrs
Required time = 10 + 3 + 2 = 15 hrs.  Two Wheeler Three Wheeler Four wheelerSpeed x (5x–20) 5xTime (t +1) tDistance 120km 120km 120km⇒ x2 – 4x – 96 = 0
∴ x = 12
 sum of the present age of mother, father and son = 42 × 3 + 6 × 3 = 126 + 18 = 144 yearsSum of the present age of family = 36 × 5 = 180Present age of bridge = 180 – 144 – 5 = 31 yearsAge of the bridge at the time of marriage = 31 – 6 = 25yrs

Ways of forming committee
1 man + 1 woman + 2 children
2 man + 1 woman + 1 child
1 man + 2 women + 1 child
Total ways,
= ^{3}c_{1} × ^{4}c_{1} × ^{2}c_{2} + ^{3}c_{2} × ^{4}c_{1} × ^{2}c_{1} + ^{3}c_{1} × ^{4}c_{2} × ^{2}c_{1}
= 3 × 4 × 1 + 3 × 4 × 2 + 3 × 6 × 2
= 12 + 24 + 36 = 72