CBSE Class 10 Mathematics Value Based Questions Set 04

VALUE BASED QUESTIONS

Q.1) Amita was given a test in mathematics by her tutor. Square of the actual marks scored by her was 9 times the marks reported by her to her parents. If the actual marks scored were 10 less than the score reported by her to the parents, then
(i) find the actual score of Amita.
(ii) Which value(s) were flouted Amita by reporting higher score to her parents.

Sol.1)(i) 15
(ii) Honesty, obedience and sincerity.
HINT:- If the actual score of Amita is x , then x =9(x+10),x >=0.

Q.2) Sham was late by 5 minutes in joing his duty on the first working day. On the second day, he was late by 10 minutes, on third day by 15 minutes and so on. After 25 working days he was shunted out of the job.
(i) Find the total working time avoided by sham.
(ii) Was the management justified in dismissing Sham?

Sol.2(i) 27 hour 5 minutes.
(ii) Yes ,the management was fully justified in dismissing Sham as he was not punctual
and wasted a lot of working time. Because of indiscipline he lost his job.
HINT:- Total time wasted=(5+10+15+.......upto 25 terms) minute
=25/2{ 2 x 5 +(25-1) x 5} minute
= 1625 minutes.

Q.3) It was required to plant trees along the sides of a quadrilateral touching a circle as shown in the figure. Distance between consecutive trees was to be kept same throughout. Two gardeners Ram and Sham were appointed by the contractor to complete the job. Ram was allotted the sides PS and QR and Sham, the other two sides. When the job was completed Ram was paid 10% more than what was paid to sham.

R

(i)Who planted more trees , Ram or Sham? 
(ii) Comment on the dealings of the contractor.

Soln.3) (i) Both Ram and Sham planted equal number of trees as PS + QR = PQ +SR.
(ii) Behaviour of contractor is not justified. Both should have been paid the same amount. Contractor is partial and irrational. 

Q.4) A straight highway leads to the foot of a tower. A watchman standing at the top of the tower observes acar at an angle of depression of 30° , which is approaching the foot of the tower with a uniform speed.Two minutes later the angle of depression was found to be 60°. The watchman suspects that some terrorists are approaching the tower. It needs half a minute for the watchman to inform the security staff to be on the alert.
(i) How much time the car will take to reach he foot of the tower.
(ii) Will the security staff be able to save the tower from the terrorists.

Sol.4) (i) one minute (ii) yes

HINT- Let MP be the tower . Let A and B are the positions of the car.Let AB=x metre

and BM = y metre and height of the tower MP= h meter.

From Δ AMP , h/x+y = tan 30° .........(i) P

From Δ BMP , h / y = tan 60° ..........(ii)

Dividing (ii) by (i) , we get

h/y x (x+y) /h = tan 60°/ tan 30°

(x+y)/y =√3/1/√3 A B M

x+y=3y

x=3y-y

x=2y

Now,speed of the car = AB/2min= x/2 m/min

Hence time taken by the car to travel from B to M 

=BM/x/2min =2y/x=1min.

Q.5 ) . A shopkeeper stopped using plastic bags & asked his customers to bring their own carry bags due to which his sales reduced by 20 units. If the square of new sales reduced by 400 gives 60 times the original sales, find his original sale.
i. Why should we ban plastic bags?
ii. What steps can be taken in order to ban plastic bags?
iii. Which trait of shopkeeper’s personality is depicted here?

Sol:5) - let the original sales be x units

Now, sales reduced by 20 units

I.e. new sales = (x - 20 units)

ATQ: (x – 20)2 – 400 = 60x

=> x² – 40x + 400 – 400 – 60x = 0

=> x² – 40x – 60x = 0

=> x² – 100x = 0

=> X(x – 100) = 0

I.e. x = 0

Or x = 100

i. Plastic is a non-biodegradable material and causes more pollution. So, its use should be restricted.

ii. We should use bags or any other substitute for plastic bags.

iii. Since the shopkeeper is working for the benefit of society on the cost of sales therefore so he is socially active and caring. 

Hence, original sale = 100 units