Tuesday, September 15, 2015

Solution of Lekhpal 2015 Exam Paper


Here I am presenting the solution Mathematics Questions, from the Question Paper of Lekhpal held on 13th September for the post in the District Lucknow on the special demand of one of our sincere visitor, Vikash. Match your answer and analyse your preparations. In case any problem you may ask for help by sending the “solution required for question no......” in comment or through forum.

Q1. The area of a rhombus is 500 cm2 and the length of one of its diagonal is 25 cm. Then the length of the other diagonal is
(a) 30 cm          (b) 20 cm          (c) 50 cm        (d) 40 cm. 

Sol. Formula:- Area of rhombus = (1/2) d1 × d2
Where d1 and d2 are the diagonals of the rhombus.
Data given:- Area = 500 cm2 and d1 = 25 cm and d2 =?
On putting and solving we get:- d2 = 40 cm.
Option (d)

Q2. The most frequently occurring value of a data set is called as
(a) Range       (b) Mode      (c) Mean             (d) Median.

Sol. The most frequently occurring of a data set is called as Mode.
Option (b)
Q3. Raghu travelled 1200 km by air which formed 2/5th of his trip. 1/3rd of the whole trip he travelled by car and rest of the journey he did by train. The distance travelled by the train is   
(a) 800 km            (b) 1800 km            (c) 480 km        (d) 1600 km

Sol.  Raghu travelled 2/5th of his trip by air = 1200 km.
Let the total trip of Raghu = x km
According  to the question:- 2/5th of trip (x) = 1200
(2/5) × x = 1200
x = 3000 km.
Now 1/3rd of the whole trip by car = (1/3) × 3000 = 1000 km
Total distance travelled by Raghu by air and car = 1200 + 1000 = 2200 km
 Remaining distance travelled by train = 3000 – 2200 = 800 km.
Hence the required distance travelled by Raghu by train = 800 km
Option (a)

Q4. The lengths of the three sides of a triangle are 35 cm, 40 cm and 45 cm respectively. The approximate area of the triangle will be  
(a) 762.82 cm2     (b) 678.82 cm2         (c) 760.82 cm2           (d) 670.82 cm2

Sol. Let the sides of a triangle be a = 35 cm, b = 40 cm, c = 45 cm
Formula used:- Area of the triangle = [s (s - a) × (s - b) × (s - c)]1/2
Where s = [(a + b + c)/2]
On solving we get Area = [60 × 25 × 20 × 15]1/2
Area = 300 × (5)1/2 = 672 cm2 (approx.)
Hence the required area = 670.82 cm2
Option (d)

Q5. The sum of three numbers is 392. The ratio of first and second number is 2:3 and that of second and third number is 5:8. Then the first number is
(a) 80                  (b) 120                      (c) 60                           (d) 100

Sol. 1st Number     2nd Number      3rd Number
                  2                      3
                                          5                         8
Equating the ratio value of 2nd Number
1st Number  :   2nd Number  :    3rd Number
          10        :              15        :            24
Let numbers be:- 1st Number = 10x,     2nd Number = 15x,       3rd Number = 24x
A.T.Q   10x + 15x + 24x = 392
                                        x = 8
Hence required First number = 10x = 10 × 8 = 80
Option (a)

Q6. A trader marks his items by increasing the price by 25%. If he gives 4% discount on the marked price, what will be his gain percentage?
(a) 25%            (b) 10%                       (c) 15%                       (d) 20%

Sol. As per concept
Percentage Gain = (+ 25) + (- 4) + [{(+ 25) × (- 4)}/100]
Percentage Gain = 25 – 4 – (100/100)
Percentage Gain = 25 – 4 – 1 = 20%
Option (d) 

Q7. The average of
n, (n + 1), (n + 2), (n + 3), (n + 4), (n + 5) is
(a) [n + (5/2)]           (b) (n + 2)         (c) 3(2n + 5)             (d) n (2)1/2

Sol. Average = [{n + (n + 1) + (n + 2) + (n + 3) + (n + 4) + (n + 5)}/6]
Average = [{6n + 15}/6]
Average = [n + (5/2)]
Option (a) 

Q8. Suresh and Sandeep are partners in a business. Suresh puts Rs. 5000/- for 5 months and Sandeep puts Rs. 6000/- for 6 months in the business. At the end of the year how much amount will Sandeep receive from a total profit of Rs. 610/- ?
(a) Rs. 360/-             (b) Rs. 410/-        (c) Rs. 380/-          (d) Rs. 400/-          

Sol. Profit Distribution Ratio = Suresh : Sandeep
Profit Distribution Ratio = 5000 × 5 : 6000 × 6
Profit Distribution Ratio =        5 × 5 : 6 × 6
Profit Distribution Ratio =            25 : 36
According to the concept of ratio and proportion Share of Sandeep in total Profit Rs. 610/-
= [{36/(25 + 36)} × 610]
= Rs. 360/-
Option (a)

Solution continues in the next post. Check it .........................

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