Modhumoti Bank PO written math 2016

Bank Written Math 2016 
 Modhumoti Bank PO written math 2016 

1. Abir can do a piece of work in 80 days. He works for 10 days and Bashir alone finish the rest of the work in 42 days. How much time would it take for the two of them together to complete the whole work?

 2. A man has to go 10 km to catch a bus. He walks part of the way at 7 km per hour runs the rest of the way at 12 km per hour. If he takes 1 hour 15 minutes to complete his journey. Find how far he walked?
3. If x + y=a, x2+y2=b2 and x3+y3=c3 then show that a3+2c3=3ab2.

4. In a school, there are equal number of boys and girls. Among the students, 1/8 of the girls and 5/6 of the boys are residing in the hostel. What percent of the Students consists of boys who do not reside in the hostel among all students?

5. ABC is a triangle in which AB = 3cm, BC = 5cm, and AC = 4cm, AD is perpendicular from A to BC. Find the length of AD.