Mu Sigma Algebra Quiz-1

given that k=(q * n - s)/ 2
2k=q * n-s
2k+s=q * n
n=(2k+s)/q so, option (a) is correct

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Option(B) is correct

Let the age be x and y years now.

Then, x−y=20 -------- (i)

and (x−5)=5(y−5) ------- (ii)

On solving both equation we get:

x=30 and y=10

Let the number of runs scored by byes, wides and runs be x,y and z respectively:

x+y+z=232 -------- (i)

The runs scored by the two batsmen are 26 times the wides:

z=26y--------- (ii)

There are 8 more byes than wides:

x=y+8 -------- (iii)

Substituting equations (iii) and (ii) in equation (i),

we get, y=8,z=208
The runs scored by Ram and Shyam were in the ratio 6:7
Let the runs scored by Ram be 6r and by Shyam be 7r.

13r=208
⇒r=16
Runs scored by Ram =16×6=96

Let, the age of Shivali be, S=11x and age of Tanisha be, T=7x.

Now, according to question after 8 years the ratio of their age become 1511.

⇒11x+87x+8=1511
⇒121x+88=105x+120
⇒x=2
Difference in ages =15×2−11×2
=8 years

Let the present age of the father and son be 17x years and 7x years.

According to Question:

(17x−6)/(7x−6)=31

Father\'s present age =17x=51 years

X coordinate has 10 possible values between -4 and 5

Y coordinate has 11 possible values between 6 and 16

1. Fix P first, P can have 10 values across X axis and 11 across Y axis. So, that\'s 11×10=110

2. Since PR is parallel to X axis, R is on the same line as P. So, R(=10−1) values left along X axis.

So far 110×9=990

3. Since PQR is a right angle triangle and the right angle is at P,PQ is parallel to Y axis. So, Q has 10(=11−1) values left.

So, 990×10=9,900

Option(B) is correct

Let the cost of each pencil be Rs x and that of each pen be y.

21x+29y=79-------- (i)

29x+21y=71-------- (iI)

On solving both equations we get:

y=2

Option(D) is correct

Let there are x first class ticket

Total cost =10x+3(18−x)
⇒10x+54−3x=110
⇒7x=56
⇒x=8
If the first class and second class tickets are interchanged.

Then total cost =10×10+3×8=124

Let the number of rows be x and number of students in each row be n.
Then, the total number of students =x×n
Again,

(n+4)(x−2)=(x−4)(n−4)=xn
⇒n=12 and x=8
Number of students =12×8=96