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Question 32 Marks
Two players: Player A and Player B are playing a game by rolling a dice. They decided that the player who will get the higher total will be the winner. In total they rolled the dice three times and the observations were recorded as follows:
Image
Answer the following questions on the basis of the information given above:
a) Who is winner of the game.
b) Represent the above information as numerical inequality.
Answer
a) Player B
b) $8<11$
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Question 42 Marks
Mr. X and Mr. Y have net worth of 1.93 crores INR and -0.22 crores INR. Represent the above information in the form of inequality.
Answer
Income of Mr. X > Income of Mr. Y; $1.93>-0.22$
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Question 52 Marks
What is the relationship between arrival time, burst time, completion time and waiting time?
Answer
Waiting time = Completion time - Arrival time - Burst time WT = CT - AT - BT
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Question 62 Marks
Prakash, Sachin and Anil started a business jointly investing 11 lakh, 16.5 lakh and 8.25 lakh respectively. The profit earned by them in the business at the end of 3 years was 19.5 lakh. What will be 50% of Anil's share in the profit?
Answer
₹ 2.25 lakh
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Question 72 Marks
A and B start a trading business with a capital of ₹ 30000 and ₹ 60000 respectively. From the profit of entire year which is ₹ 18000, A gets ₹ 8500 as his share of profit and salary for managing the business. What is the amount that A receives as his salary?
Answer
2500
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Question 82 Marks
What is the investment ratio of A,B and C if their profit ratio is 6:7:8 respectively and their investment time period ratio is 2:3:4 respectively?
Answer
$9: 7: 6$
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Question 92 Marks
Priya started a tiffin service business by investing 40000. After 4 months her friend Rekha joined her business and invested 50000 in it. What will be the share of Rekha in the profit if they earn220000 as profit in the entire year?
Answer
₹ $1,00,000$
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Question 102 Marks
In a 200 metresrace, Prateek beats Samarth by 35 metres or 7 seconds. How much time did Prateek take to cover the race?
Answer
33 seconds
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Question 112 Marks
A team played 40 games in a season and lost in 16 of them. What percent of games played did the team win?
Answer
60\%
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Question 122 Marks
A runs 3 times as fast as B. If A gives B a start of 40metres, how far must the goal on the race course be so that A and B reach the goal at the same time?
Answer
60meters
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Question 132 Marks
In a 500 metres race, A defeats B by 60 metres (or) 12 seconds. What is the time taken by A to complete the race?
Answer
88 seconds
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Question 142 Marks
A cistern can be filled in 8 hours but due to a leakage in its bottom, it takes 2 hours more to fill the tank. If the cistern is full, how much time will the leakage take to empty it?
Answer
40 hours
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Question 152 Marks
A cistern can be filled by pipes A and B in 4 hours and 6 hours respectively. When full, the cistern can be emptied by pipe C in 8 hours. If all the pipes were turned on at the same time, in how much time will the cistern be filled?
Answer
3 hrs 25 minutes
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Question 162 Marks
A pipe can fill a cistern in 6 hours. Due to a leakage in the tank the cistern is just full in 9 hours. How much time the leakage will take to empty the tank?
Answer
18 hrs
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Question 172 Marks
Pipe A can fill a tank in 30 hours and pipe B in 45 hours. If both the pipes are opened in an empty tank, how much time will it take to fill the tank?
Answer
18 hrs
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Question 182 Marks
A man can row 7 km per hour in still water. If the stream is flowing at the rate of 5 km per hour, it takes him 7 hours to row to a place and return, how far is the place?
Answer
12 km
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Question 192 Marks
The speed of a boat in still water is 14 km per hour. While going downstream it moves at the rate of 24 km per hour. Find the speed of the boat against the stream.
Answer
4 km/
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Question 202 Marks
Find the speed of the boat, if a boat moves downstream at the rate of 16 km/hr and upstream at the rate of 10 km/hr.
Answer
13 km/h
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Question 212 Marks
In what ratio, water must be added to dilute honey costing ₹ 240 per litre so that the resulted syrup would be worth ₹ 200 per $l$ ?
Answer
1 : 5
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Question 222 Marks
600 gm of jaggery syrup has $40 \%$ jaggery in it. How much jaggery should be added to make it $50 \%$ in the syrup?
Answer
120 g
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Question 232 Marks
Cost of two types of pulses is ₹ 55 per kg and ₹ 90 per kg . If both the pulses are mixed together in the ratio $2: 3$, what should be the price of the mixed variety of pulses per kg ?
Answer
₹ 76
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Question 242 Marks
A container contains $70 /$ of orange squash. The squash being too concentrated $7 /$ of squash was taken out from this container and replaced by water. This process was repeated thrice to reduce the concentration of squash. How much quantity of orange squash is left in the container?
Answer
51.03 litres
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Question 252 Marks
The average salary per head of the entire staff of a small factory including the supervisor and labours is ₹ 5750 . The average salary per head of the supervisor is ₹ 20,000 and that of the labours is ₹ 5000 . Find the number of labours in the factory if there are 4 supervisors.
Answer
₹ 76
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Question 262 Marks
In what ratio must rice at ₹ 69 per kg be mixed with rice ₹ 100 per kg so that the mixture be worth ₹ 80 per kg?
Answer
20 : 11
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Question 292 Marks
There are 81 boxes with 21 articles in each. When we rearrange all of the articles so that each box has 5 articles, how many articles will be left out without a box.
Answer
1
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Question 352 Marks
What time will it be after 1250 hours, If the present time is 9:00 pm?
Answer
Number of hours in a day $=24$ hours
$
1250(\bmod 24)=2 \quad \text { (as } 1250 \text { hours }=52 \text { days }+2 \text { hours })
$
Therefore, it will be $11: 00 pm$ after 1250 hours.
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Question 362 Marks
Apply multiplication modulo on positive integers 5 and 3 for modulo 25
Answer
Given $a =5, b=3, m=25$ then $\quad a \odot_{ m } \quad b =5 \odot_{25} \quad 3=15( as \quad ab =15<25)$
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Question 372 Marks
If $a=3, b=11, m=8$, then find $a \odot_{ m } b$
Answer
$\begin{array}{l}\text { Given } a =3, b=11, m=8 \\ a \odot_{ m } b =3 \odot_8 \quad 11=1\end{array}$
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Question 382 Marks
Find $a -_{ m } b$, if $a =11, b=43$ and $m =7$
Answer
As, $a=11, b=43$ and $m=7$
then, $a-_m b=11-43=(11-43) \bmod 7$
$-32 \bmod 7=3$
$
(\text { as }-32=7 \times(-5)+3)
$
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Question 392 Marks
Find $a -_{ m } b$, if $a =17, b=13$ and $m =3$
Answer
As, $a=17, b=13$ and $m=3$ then, $a -{ }_{ m } b =17-13=1 \quad($ as $a - b =17-13=4>3)$
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Question 402 Marks
Apply subtraction modulo to positive integers 15 and 6 for modulo 25
Answer
Here $a=15, b=6, m=25$
then, $a - m b =15-_{25} 6=9($ as $a - b =9 < 25)$
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Question 412 Marks
Find subtraction modulo 8 if a and b are 11 and 3 respectively.
Answer
Given $\quad a =11, b=3, m=8$
$
a-_{m} b=11-_8 3=0(\text { as } a-b=8=m)
$
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Question 422 Marks
Apply addition modulo to positive integers 17 and 13 for modulo 30.
Answer
Let $a =17, b=13$ and $m =30$
$
a+_{m} b=17+_{30} 13=0 \quad(\text { as } a+b=17+13=30 ; 30 \bmod 30=0)
$
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Question 432 Marks
Find addition modulo 25 where a and b are 15 and 6 respectively
Answer
Here $a =15, b=6, m=25$
Therefore $a+_m \quad b=15+_{25} 6=21$
(as a + b $=21<25$ )
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Question 442 Marks
Find addition modulo 8 if a and b are 3 and 11 respectively
Answer
Given $a =3, b=11, m=8$
Hence $a+_m \quad b=3+_8 \quad 11=6$ as $a + b =14>8$
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Question 452 Marks
Verify (14 x 8) mod 5 = (14 mod 5 x 8 mod 5) mod 5
Answer
L.H.S. $(14 \times 8) \bmod 5=112 \bmod 5=2$
R.H.S. $(14 \bmod 5 \times 8 \bmod 5) \bmod 5=(4 \times 3) \bmod 5=12 \bmod 5=2$
L.H.S. $=$ R.H.S. Hence verified
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Question 462 Marks
Consider the below processes available in the ready queue for execution, with arrival time as 0 for
all and given burst time. Find the average waiting time using the SJF scheduling algorithm.
Image
Answer
In SJF, the shortest process is executed first, the GANTT chart for given process is
Image
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Question 482 Marks
Verify that (14 + 8) mod 5 = (14 mod 5 + 8 mod 5) mod 5
Answer
L.H.S. $(14+8) \bmod 5=22 \bmod 5=2$
R.H.S. $(14 \bmod 5+8 \bmod 5) \bmod 5=(4+3) \bmod 5=7 \bmod 5=2$
L.H.S. = R.H.S. Hence verified
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Question 492 Marks
Divide a net profit of 21000 among three partners A,B,C in a business whose capital investments
were 36000, 42000 and 48000 respective
Answer
on: Ratio of the capitals is 36000:42000:48000 or 6:7:8
The profit is divided in the ratio of capitals, there
A's share ₹ $\frac{21000 \times 6}{21}=$ ₹ 6000
B's share ₹$\frac{21000 \times 6}{21}=$ ₹ 7000
C's share ₹$\frac{21000 \times 8}{21}=$ ₹ 8000

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Question 502 Marks
P,Q and R jointly invested a total of 64000 in a business. P invested 6000 more than Q and Q
invested 5000 more than R. Find the ratio of their capital?
Answer
Let the investment of $R$ is ₹ $x$, then the investment of $Q$ and $P$ is ₹ $(x+5000)$ and $₹(x+11000)$ respectively.
According to the question,
$
\begin{array}{l}
x+x+5000+x+11000=64000 \\
3 x=48000 \\
x=16000
\end{array}
$
The ratio of the capitals of $P, Q$ and $R$ is 27000:21000:16000 or 27:21:16
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2 Marks Questions - Applied Maths STD 12 Science Questions - Vidyadip