1. Two neighbors Mrinalini and Harsha decided to play a dice game with each other. They rolled dice one after the other. The probability that the number value of the dice rolled first is smaller than the number value of the second is:
a) 3/13
b) 7/36
c) ¼
d) 5/12
e) 7/12
2. Subham and Akarsh start a retail chain partnership. Subham invested Rs. 16000 and Akarsh invested Rs. 12000 initially. Due to personal causes, Subham withdrew Rs. 5000. Due to the withdrawal of sums by Subham, Akarsh invested Rs. 5000 more to keep up the costs of business. After three more months, Shaurya joined the partnership with a capital investment of Rs. 21000. The share of Akarsh exceeds the share of Shaurya out of a total profit of Rs. 72900 after one year by:
a) 41500
b) 12150
c) 76000
d) 57000
e) None of the above
3. Mr. Thakre left his property in a will of Rs. 35 lakhs between his two sons. The elder son is 16 years old and the younger is 7. 5 years younger than the earlier. The property was divided in such a way that the two sons get equal amounts when they reach 21 years of age each. The original amount of property was instructed to be invested at 10 % p. a Simple interest. Determine how much money the elder son will get at the time of the declaration of the will.
a) 17. 5 lakhs
b) 21 lakhs
c) 20 lakhs
d) 15 lakhs
e) Cannot be determined
4. Two retailers Garry and Cisco put up a stall in a trade fair to sell their typewriters. Both of them each typewriter at Rs. 1800 each. The profit percent by both the retailers is same but Garry calculates his profit on selling price and Cisco calculates his profit on cost price which is equal to a profit of 20%. What is the difference in their actual profits?
a) Rs 300
b) Rs 100
c) Rs 70
d) Rs 400
e) Rs 60
5. Sonia’s math’s teacher gave her a task to choose one natural number at random from first 100 natural numbers The probability that x+(100/x)>50 is:
a) 1/10
b) 11/20
c) 17/32
d) 19/31
e) None
6. Abbas micro financial services, a private financing firm in Surat lends an equal sum of money at the same rate of interest to Banshee and Shyam. The money given to Banshee becomes twice of the original amount in just four years at simple interest. While Abbas services lend to Shyam for first two years at compound interest and for the rest two years at simple interest. If the difference between the amount of Banshee and Shyam after 4 years is Rs 2750. What is the amount of money lent to each Banshee and Shyam?
a) Rs. 40000
b) Rs 4000
c) Rs 75000
d) Rs 8000
e) Rs 89000
7. Ram was traveling in a boat when the wind blew his cap off and the cap started floating back downstream. The boat continued to travel upstream for 12 more minutes before Ram realized that his cap had fallen off and turned back downstream. He caught up with that as soon as it reached the starting point. Find the speed of river if Ram’s cat flew off exactly 3 km where he arrived.
a) 5kmph
b) 6kmph
c) 10kmph
d) 7. 5kmph
e) Cannot be determined
8. Gopal, Bheem, and Krishna are three miners employed by a mining contractor. They mine a complete coal field in 10 days. Initially, all of them worked together but the last 60% of the work was completed by only Bheem and Krishna together. Gopal worked with Bheem and Krishna only for initial 2 days then he left the work due to poor health. Also, Bheem takes 20% less time to finish the work alone than that of Krishna working alone. If they were paid Rs 3000 for the entire mining of the coal field, then what is the share of the least efficient miner?
a) Rs 900
b) Rs 1200
c) Rs 1000
d) Rs 5000
e) None of these
9. Madhu and Madan have a rectangular field of area 20000 sq. m. They decided to divide it into two equal parts by dividing it with a straight line. Madhu wanted to fence their land immediately, so they incurred total expenses for the fencing all the four sides alone at Rs. 2 per meter. What is the minimum cost that Madhu had to incur?
a) Rs. 800
b) Rs. 1600
c) Rs. 2000
d) Rs. 6500
e) Rs. 600
10. Birla and Ratan bought two rectangular fields of the same area in the countryside. The length of the rectangular field bought by Birla is x% less than the length of the field bought by Ratan and breadth of the first field is 5x % greater than the breadth of the second field. What is the value of x?
a) 80
b) 25
c) 15
d) 50
e) 45
Answers & Explanations:
1.
Answerd
The number value of the dice rolled first is smaller than the number value of the second means the following cases:
Dice1 Dice2
1 no value lesser than one
2 1
3 1,2
4 1,2,3
5 1,2,3,4
6 1,2,3,4,5
Hence 15 such possible cases exist.
Probability=possible cases/total sample space
=15/36=5/12 (ans)
2.
Answere
Subham

Akarsh

Shaurya
 
After 3 months

16000x3

12000x3



After 3 months

11000x9

17000x9



After 3 months

“

“

21000x6

Profit share

16x3+11x9

12x3+17x9

21x6

Ratio

7

9

6

Difference of shares of Akarsh and Shaurya=96=3
Hence difference of their profits= 3/22 x 72900= Rs. 40500 (Ans)
3.
Ansb
Solve by options
In option b, let elder son get 21 lakhs, then younger gets 14 lakhs
According to the question,
After when both sons attain the age of 21 years, they both will get the same amount of money.
Hence for the elder son, the money gets invested for 5 years and for younger son the money is invested for 12.5 years at 10 % S.I.
Hence at 21 years the elder son will get=
21+(50/100)x21=31.5 Lakhs
At 21 years, the younger son will get=
14+(125/100)x14=31.5 Lakhs
Hence the condition is satisfied.
Option B=21 lakhs is the answer
4.
Answere
Profit of Garry ( on selling price) = 20/100 x 1800= Rs 360
Given for Cisco=> 120% of CP=1800
Dividing both sides by 6 we get,
20% of CP=300
Hence Profit=300
Profit GarryProfit Cisco=360300= Rs 60 (Ans)
5.
Answerb
Total sample space=100
Given condition: x+(100/x)>50
On solving , x2+10050x>0
We get 2.(something)>x>47.(something)
Hence x has 55 satisfied values
Probability= 55/100=11/20 (ans)
6.
Ansd
Banshee:
P=(Px4xr)/100=>r=25%
Shyam:
P(1+25/100)2 =25P/16
Again,
25P/16 x (2x25)/100 = 25P/32
Therefor total amount of banshee after 4 years=2P
Tota amount of Shyam after 4 years= 25P/16 + 25P/32 = 75P/32
Therefore difference in amount= 75P/32  2P= 11P/32 =2750
=>P=Rs.8000
7.
Ansd
Let the speed of the boat be B and that of the river be R.
In 12 minutes the distance between boat and cap=12(BR)+12R=12B
Now time taken by boat to reach the cap= 12B/{(B+R)R)}=12 minutes
Total time=24 minutes
In 24 minutes the cap flew= 3km
So, 24/60 x R=3
=> R=7.5 kmph
8.
Ans c
Initial 2 days (G+B+K=40%) +last 8 days(B+K=60%)
The efficiency of B and K is 7.5 %, Since B and K complete 60% work in 8 days and efficiency of G,B and K is 20%. It means efficiency of G alone is 12.5%= 207.5%
Now,
Number of days= 4x : 5x ( B:K)
Efficiency= 5y:4y (B:K)
Efficiency of B=5/9 x 7.5= 4.16%
Efficiency of K= 4/9 x 7.5=3.33%
Hence K(Krishna) has the least efficiency
Share of work done by him= 3.33% x 10 = 33.33%
Share of amount= 33.33% of Rs 3000 = Rs 1000
9.Ans C
Length x breadth=2000
=>L/2 x b=10000=Area of Madhu’s land
For the given area, a square gives the minimum perimeter
L/2=b
=>bxb=10000
=>b=100m
Perimeter=4x100=400m
Expenses of fencing=5x400=Rs.2000
10. Ans A
Solve by options
Let the length and breadth of the second rectangle is l and b respectively, Then the area of the second field is l x b
In option a, x=80, then, area of first field= l/5 x 5b=lb
Hence the area of Birla’s field =area of Ratan’s field.