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Question 1 of 5
1. Question
The value of k, for which the system of equations 3xky20=0 and 6x10y+40 = 0 has no solution, is
Correct
Ans: c
For no solution, a_{1}/a_{2} = b_{1}/b_{2} ≠ c_{1}/c_{2}
∴3/6 =( k/10) ≠ (20/40) ⇒ k = (3×10)/6 = 5
Incorrect
Ans: c
For no solution, a_{1}/a_{2} = b_{1}/b_{2} ≠ c_{1}/c_{2}
∴3/6 =( k/10) ≠ (20/40) ⇒ k = (3×10)/6 = 5

Question 2 of 5
2. Question
There are three brothers. The sums of ages of two of them at a me are 4 yr, 6 yr and 8 yr. The age difference between the eldest and the youngest is
Correct
Ans: b
Let the ages of three brothers be a, b and c
Then, a+b = 4, b+C = 6 and c+ a = 8
On solving these three equations, we get
a = 3, b = 1 and c = 5
∴Age difference between eldest and youngest
= 5 1 = 4yr
Incorrect
Ans: b
Let the ages of three brothers be a, b and c
Then, a+b = 4, b+C = 6 and c+ a = 8
On solving these three equations, we get
a = 3, b = 1 and c = 5
∴Age difference between eldest and youngest
= 5 1 = 4yr

Question 3 of 5
3. Question
Let a two digits number be k times the sum of its digits. If the number formed by interchanging the digits is m times the sum of the digits, then the value of m is
Correct
Ans: c
Let the unit’s place number be y and ten’s place number De x.
Then, number = 10x+ y
Now, after interchanging the digits,
New number = 10y+ x and sum of digits = x+ Y
According to the question,
10x + y=k(x + y) ……………………………………………………….(1)
and
10y+x =m(x + Y)………………………………………………………..(2)
On adding Eqs. (1) and (2), we get
11(x+y)= (k + m) (x + y) ⇒ k+ m = 11m⇒11 K
Incorrect
Ans: c
Let the unit’s place number be y and ten’s place number De x.
Then, number = 10x+ y
Now, after interchanging the digits,
New number = 10y+ x and sum of digits = x+ Y
According to the question,
10x + y=k(x + y) ……………………………………………………….(1)
and
10y+x =m(x + Y)………………………………………………………..(2)
On adding Eqs. (1) and (2), we get
11(x+y)= (k + m) (x + y) ⇒ k+ m = 11m⇒11 K

Question 4 of 5
4. Question
The annual incomes of two persons are in the ratio 9 :7 and their expenses are in the ratio 4:3. If each of them saves 2000 per year, then what is the difference in their annual incomes?
Correct
Ans: a
Let annual incomes of two persons be 9x and 7x and expenses
be 4y and 3y, respectively.
Then, according to the question,
9x4y=2000 ……………………………………………………………….(1)
and 7x3y = 2000 ……………………………………………………..(2)
From Eqs. (1) and (2), we get 9x – 4y = 7x – 3y
y= 2x
On putting the value of y in Eq. (1), we get
9x – 8x = 2000 ⇒ x =Rs. 2000
∴Difference between their annual incomes
= 9x7x = 2x = Rs. 4000
Incorrect
Ans: a
Let annual incomes of two persons be 9x and 7x and expenses
be 4y and 3y, respectively.
Then, according to the question,
9x4y=2000 ……………………………………………………………….(1)
and 7x3y = 2000 ……………………………………………………..(2)
From Eqs. (1) and (2), we get 9x – 4y = 7x – 3y
y= 2x
On putting the value of y in Eq. (1), we get
9x – 8x = 2000 ⇒ x =Rs. 2000
∴Difference between their annual incomes
= 9x7x = 2x = Rs. 4000

Question 5 of 5
5. Question
If (p/x)+(q/y) =m and (q/x)+(p/y) = n, then what is x/y equal to?
Correct
Ans: c
Given, (p/q) + (q/y) = m and (q/x) +(p/y) =n
Let 1/x = u and 1/y = v
Then, pu+qv = m ………………….(1)
And qu+pv = n ………………………(2)
On solving Eqs.(1) and(2), we get
∴u = (mp – nq)/(p2 – q2) and v = [(mq/q2)(q2p2)]
∴x/y = (1/u)/(1/v) = v/u = (mpnq)/(mpnq) = (nqmq)/mpnq)
Incorrect
Ans: c
Given, (p/q) + (q/y) = m and (q/x) +(p/y) =n
Let 1/x = u and 1/y = v
Then, pu+qv = m ………………….(1)
And qu+pv = n ………………………(2)
On solving Eqs.(1) and(2), we get
∴u = (mp – nq)/(p2 – q2) and v = [(mq/q2)(q2p2)]
∴x/y = (1/u)/(1/v) = v/u = (mpnq)/(mpnq) = (nqmq)/mpnq)
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