[4 marks sum]

Question 14 Marks

How will Rs 31500 be shared between A, B, and C; if A gets the double of what B gets, and B gets the double of what C gets?

Answer

Let the share of $C=1$
Share of $B=$ double of $C=2 \times 1=2$
Share of $A=$ double of $B=2 \times 2=4$
Given ratio $(A: B: C)=4: 2: 1$
Sum of ratio $=4+2+1=7$
A's share $=\frac{4}{7} \times \operatorname{Rs} 31500$
$=4 \times \operatorname{Rs} 4500=\operatorname{Rs}=18000$
B's share $=\frac{2}{7} \times$ Rs 31500
$=2 \times \operatorname{Rs} 4500=\operatorname{Rs} 9000$
C's share $=\frac{1}{7} \times$ Rs 31500
$=1 \times \operatorname{Rs} 4500=\operatorname{Rs}=4500$

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Question 24 Marks

A profit of Rs 2,500 is to be shared among three persons in the ratio 6 : 9 : 10. How much does each person get?

Answer

Total profit $=$ Rs 2,500
Given ratio $=6: 9: 10$
Sum of ratio $=6+9+10=25$
Share of 1 st person $=\frac{6}{25} \times 2500$
$=6 \times 100=$ Rs 600
Share of 2 nd person $=\frac{9}{25} \times 2500$
$
=9 \times 100=\operatorname{Rs} 900
$
Share of 3rd person $=\frac{10}{25} \times 2500$
$
=10 \times 100=\operatorname{Rs} 1000
$

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Question 34 Marks

$\text { Divide Rs } 10,400 \text { among A, B and C in the ratio } \frac{1}{2}: \frac{1}{3}: \frac{1}{4}$

Answer

$\text { Given ratio }=\frac{1}{2}: \frac{1}{3}: \frac{1}{4}$
$=\frac{1}{2} \times 12: \frac{1}{3} \times 12: \frac{1}{4} \times 12 \ldots \ldots . .(\text { Since L.C.M. of } 2,3 \text { and } 4=12 \text { ) }$
$=6: 4: 3$
Sum of ratio $=6+4+3=13$
A's part $=\frac{6}{13} \times 10400=6 \times 800=4800$
B's part $=\frac{4}{13} \times 10400=4 \times 800=3200$
C's part $=\frac{3}{13} \times 10400=3 \times 800=2400$

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Question 44 Marks

Mr. Gupta divides Rs 81000 among his three children Ashok, Mohit, and Geeta in such a way that Ashok gets four times what Mohit gets and Mohit gets 2.5 times what Geeta gets. Find the share of each of them.

Answer

Let the share of Geeta $=1$
Share of Mohit is (2.5 times of Geeta) $=2.5$
Share of Ashok is ( 4 times of Mohit) $=4 \times 2.5=10$
Ratio $=1: 2.5: 10=1 \times 2: 2.5 \times 2: 10 \times 2=2: 5: 20$
Sum of ratio $=2+5+20=27$
Share of Geeta $=\frac{2}{27} \times$ Rs $81000=2 \times$ Rs $3000=\operatorname{Rs} 6000$
Share of Mohit $=\frac{5}{27} \times$ Rs $81000=5 \times \operatorname{Rs} 3000=$ Rs 15000
Share of Ashok $=\frac{20}{27} \times \operatorname{Rs} 81000=20 \times \operatorname{Rs} 3000=\operatorname{Rs} 60000$

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Question 54 Marks

In a club has 360 members, 40 play carrom, 96 play table tennis, 144 play badminton, and remaining members play volley-ball. If no member plays two or more games, find the ratio of members who play:
(i) carrom to the number of those who play badminton.
(ii) badminton to the number of those who play table-tennis.
(iii) table-tennis to the number of those who play volley-ball.
(iv) volleyball to the number of those who play other games.

Answer

Total members in a club = 360 members
Members who play carrom = 40
Members who play table tennis = 96
Members who play badminton = 144
Members who play volleyball = 360 – (40 + 96 + 144) = 360 – 280 = 80
(i) Ratio between the members who play carrom to the number of those who play badminton = 40 : 144 ⇒ 5 : 18
(ii) Ratio of members who play badminton to the number of those who play table- tennis = 144 : 96 ⇒ 6 : 4 = 3 : 2
(iii) Ratio of members who play table tennis to the number of those who play volley-ball = 96 : 80 ⇒ 6 : 5
(iv) Ratio of members who play volley-ball to the number of those who play other games = 80 : 280 ⇒ 4 : 14 = 2 : 7

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Question 64 Marks

Rohit goes to school by car at $60\ \text{km}$ per hour and Manoj goes to school by scooty at $40\ \text{km}$ per hour. If they both live in the same locality, find the ratio between the time taken by Rohit and Manoj to reach school.

Answer

Rohit travel by car, speed of the car $=60 km / hr$
Manoj travel by scooty, speed of the scooty $=40 km / hr$
Since, It is given that, they live in the same locality
Hence, let the distance be k Time taken by Rohit to reach school
$=\frac{\text { Distance }}{\text { Speed }}$
$=\frac{K}{60}$
Time taken by Manoj to reach school $=\frac{ K }{40}$
$\therefore$ The ratio between the time taken by Rohit and Manoj to reach school
$=\frac{K}{60}: \frac{K}{40} $
$=\frac{1}{3}: \frac{1}{2}=2: 3$

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Question 74 Marks

In winter, a school opens at 10 a.m. and closes at 3.30 p.m. If the lunch interval is of 30 minutes, find the ratio of lunch interval to total lime of the class periods.

Answer

Timing of a school (10 a.m. to 3.30 p.m) = 5 hours 30 minutes
Timing for lunch interval = 30 minutes
Total time of the class periods = 5 hours 30 minutes – 30 minutes
= 5 hours = 60 × 5 = 300 minutes
Ratio of lunch interval to total time of the class period = 30 minutes : 300 minutes = 1 : 10

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Question 84 Marks

The student-teacher ratio in a school is 45 : 2. If there are 4050 students in the school, how many teachers must be there?

Answer

Total number of students $=4050$
Let the total number of teachers $=x$
The student-teacher ratio in a school $=45: 2$
$\therefore$ Required ratio $=\frac{\text { Total number of students }}{\text { Total number of teachers }}$
$\Rightarrow \frac{45}{2}=\frac{4050}{ x }$
$\Rightarrow x=\frac{4050 \times 2}{45}=180$ teachers
$\therefore$ Number of teachers $=180$

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Question 94 Marks

Ratio of the distance of the school from A’s home to the distance of the school from B’s home is 2 : 1.
(i) Who lives nearer to the school?
(ii) Complete the following table:

Answer

Ratio of the distance of the school from A's home to the distance of the school from B's hence $=2: 1$
(i) B lives nearest to the school
(ii) Let A's home is $2 x km$ from school and B's home is $x km$
Distance of school from A's home $=2 x$ Distance of school from B's home
$\Rightarrow$ If $A$ lives at a distance of $4 km$, then $B$ lives at a distance of $=\frac{1}{2} \times 4=2 km$
$\Rightarrow$ If $B$ lives at a distance of $9 km$ then $A$ lives at a distance of $=2 \times 9=18 km$
$\Rightarrow$ If $A$ lives at a distance of $8 km$ then $B$ lives at a distance $=\frac{1}{2} \times 8=4 km$
$\Rightarrow$ If $B$ lives at a distance of $8 km$, then $A$ lives at a distance $=2 \times 8=16 km$
$\Rightarrow$ If $A$ lives at a distance of $6 km$, then $B$ lives at a distance $=\frac{1}{2} \times 6=3 km$

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MATHS [4 marks sum]

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