**Question-1****Explanation**

**Mr. Dileep sarkar has a rectangular housing plot in Hakimpara, Jalpaiguri. The area and the perimeter of his plot are 525 sq.m. and 100 metres respectively. What is the ratio of length to breadth of this rectangular plot owned by Mr. Dileep Sarkar?**

**Options :**

a)7:4

b)8:3

c)7:2

d)7:3

**Answer: d) 7:3**

Let the length of the rectangular plot be x

Let the breadth of the rectangular plot be y

Then area of the rectangular plot = length x breadth= xy

Perimeter of the rectangular plot=2(x+y)

X Yis given as 525 sq.m

And 2(x+y)=100m

Therefore (x+y)= 50m…..(1)

(x-y)^2=(x+y)^2-4xy

(x-y)^2=(50)^2-4*525=2500-2100=400

(x-y)=√400=20….(2)

Solving (1)and (2) x+y-x+y=50-20=30

2y=30

So y=15m and x=35m

Length: breadth=35m:15m=7:3

**Question-2****Explanation**

** Anna river is one of the rivers in Michigan district, USA, Mr. Black sails his boat at 25km per hour in still water. The speed of Anna river stream is 5km per hour. Mr. Black takes 2.5 hours to go upstream than going the same distance downstream. (from P to Q). How far is Q from P?**

**Options :**

a)120km

b)150km

c)140km

d)200km

**Answer: b) 150km **

Let the distance from P to Q be x km

It takes 2.5 hours more to travel upstream than downstream from p to Q and return.

Upward speed of the boat will b=25-5=20 km/hour

Downward speed of the boat will be=25+5=30 km/hour

Then x/20-x/30=2.5

(3x-2x)/60=2.5

x/60=2.5

x=60*2.5=150km

**Question-3****Explanation**

** Sureshkumar, Govindasamy, raachandran take a contract work for Rs. 4465 lakhs. Sureshkumar and Ramachandran take up 12/19 of the work and complete it by themselves. The bill was submitted by them to the authorities and they suggested separate payment for
govindasamy may be made for the work done by hem. How much will paid to Givindasamy?**

**Options :**

a)Rs.465 lakhs

b)Rs.1465lakhs

c)Rs.1782 lakhs

d)Rs. 1645 lakhs

**Answer: d) 1645 lakhs **

Sureshkumar and Ramachandran perform 12/19 of the work contracted.

So part of work done by Govindasamy= 1-12/19=7/19

Total contract for the work=Rs. 4465 lakhs

Govindasamy is to be paid for 7/19 of work=4465*7/19=Rs. 1645 lakhs.

**Question-4****Explanation**

** Pramod Khanna and Akshay Bachchan can do a work in 40 and 25 days respectively. They began the work together, but Pramod Khanna left after some days and akshay Bachchan finished the remaining work in 12 days. After how many days did Pramod Khanna leave?**

**Options :**

a)8 days

b)10 days

c)9 days

d)12 days

**Answer: a) 8 days. **

Pramod Khanna and Akhy Bachchan can do the work in 40 days and 25 days respectively.

Pramod Khanna will do in one day-1/40 of the work

Akshay Bachchan will do in one day-1/25 of the work

If they work together they will do in one day-(1/40+1/25)of the work =13/200 of the work,

Akshay Bachchan has completed the work in 12 days after Pramod Khanna leaving the work in the middle.

Akshay Bachchan can do in one day-1/25 of the work

So in 12 days he would have 1/25*12=12/25 of the work

So work completed by Pramod Khanna and akshaya Bachchan together is 1-12/25=13/25

These two can do in one day 13/200 of the work

They have completed together 13/25 of the work

So number of days they worked together-13/25 divided by 13/200=13/25*200/13=8 days.

**Question-5****Explanation**

** Ashudeep started a stationery shop in Big Bazzar, Madurai, He bought 80 pencils for Rs. 200. How many pencils must be sld for Rs. 100 in order to get 25% profit?**

**Options :**

a)30

b)32

c)24

d)28

**Answer: b)32 **

Ashudeep purchases 80 pencil for Rs. 200.

So cost of one pencil=Rs. 2.50

In order to earn 25% profit each pencil should be sold at 2.50*1.25

So for Rs. 100 he should sell=(100)/2.50*1.25= 32 pencils.