algebraic expressions Model Questions & Answers, Practice Test for ssc mts paper 1 2023

Answer: (b)

Let the present ages of Mr. Ramesh and his son be x and y respectively.

∴ x = 4y and (x + 10) = 2(y + 10) Solving the above two equations, we get x = 20 years and y = 5 years

Answer: (a)

2x + y = 17 ⇒ y = 17– 2x ...... (i)

y + 2z = 15 ⇒ 17 – 2 x + 2z = 15

⇒2x – 2z = 2 ⇒ x – z = 1 ...... (ii)

and x + z = 9 ...... (iii)

Solving equations (i) and (ii), we get

x = 5, z = 4

∴ y = 17 – 2x = 17 – 10 = 7

4x + 3y + z = 4 × 5 + 3 × 7 + 4

= 20 + 21 + 4 = 45

Answer: (a)

P (P – 3) < 4 (P – 3);

P (P – 3) – 4 (P – 3) < 0

(P – 3) (P – 4) < 0

This means that when

(P – 3) > 0 then (P – 4) < 0 ........(i)

or, when (P – 3) < 0 then (P – 4) > 0 ........(ii)

From (i),

P > 3 and P < 4

∴ 3 < P < 4

From (ii)

P < 3 and P > 4

Answer: (c)

Let the first, second, third and fourth numbers be a, b, c and d respectively.

According to the question,

a + b + c + d = 64 ....(i)

and a + 3 = b – 3 = 3c = $d/3$

i.e., a + 3 = b – 3 ⇒ b = a + 6 ....(ii)

Also, c = ${a+3}/3$ and d = 3 ( a + 3)

Solving the above eqns, we get

a = 9, b = 15, c = 4 and d = 36

∴ Difference between the largest and the smallest numbers = 36 – 4 = 32

Answer: (b)

Suppose the two-digit number be 10x + y.

Then we have been given

l0x + y – (10y + x) = 9

⇒9x – 9y = 9

⇒x – y = 1

Hence, the required difference = 1 Note that if the difference between a two-digit number and the number obtained by interchanging the digits is D, then the difference between the two digits of the number = $D/9$