[Mission 2023] Insta–DART (Daily Aptitude and Reasoning Test) 10 June 2023

Ans: c

For no solution, a₁/a₂ = b₁/b₂ ≠ c₁/c₂

∴3/6 =( -k/-10) ≠ (-20/40) ⇒ k = (3×10)/6 = 5

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

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

Ans: a

Let annual incomes of two persons be 9x and 7x and expenses

be 4y and 3y, respectively.

Then, according to the question,

9x-4y=2000  ……………………………………………………………….(1)

and  7x-3y = 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

= 9x-7x = 2x = Rs. 4000

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)-(q2-p2)]

∴x/y = (1/u)/(1/v) = v/u = -(mp-nq)/(mp-nq) = (nq-mq)/mp-nq)