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Correct option is C)
Let be students are consider as child
Let the age of child added later be x years.
average age of 12 children =20 years
∴ Total age of 12 children =20×12=240 years
After one more child is added-
Average of 13 children =20−1=19 years
Average age of 13 children =
13
sum of 12 children+x
​

19=
13
240+x
​

⇒240+x=247
⇒x=247−240=7 years
Hence the age of child added later is 7 years.

23

Time taken to fill repaired cistern = 12 mins

In 1 min, pipe will fill = 1/12

Time taken to fill cistern with leak = 12 + 18 = 30 mins

In 1 min, it will fill = 1/30

Consider the leak as an outlet pipe, so

1/30 = 1/12 – [ in 1 min how much the outlet pipe leaks ]

= 1/12 – 1/30

= 5/60 – 2/60 = 3/60 = 1/20

Therefore, it will take 20 mins for the leak to empty the cistern

( b ) P

let the speed limit be x.
speed by first rider S1 and 2nd rider be S2.
S1=x+10;
ans S2=x+2*10; and given S2=35.
solving we get x=15mph.

Doug won the race
Explanation-
The ratio of steps covered by me, Doug, and Anne is = 6:7:8

Since Distance covered in Me 21 steps = Distance covered by Doug 24 steps = Distance covered by Anne 28 steps

LCM (21, 24, 28) = 168

For a distance of 168 units, the ratio of the distance covered in each step is;
= 8 : 7 : 6
Therefore the ratio of speeds is;
= 8×6: 7×7: 6×8
= 48 : 49 : 48

Here, the speed of the Doug is more than the speed of me and Anne
Hence, Doug won the race

28
to arrange m objects in n places => nCm
i.e. for this example m=2(+,- sign) and n = 8(places between two number from 1 to 9)
SO, answer is : 8C2 = (8*7) / 2 = 28

8:7 ratio

11

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