time and work Model Questions & Answers, Practice Test for ssc mts tier 1 2024

Answer: (c)

${(x + 2)(x - 3)}/{(x + 4)(x - 2)} = {x^2 - x - 6}/{x^2 + 2x - 8} = 3/4$

⇒$4x^2 – 4x –24 = 3x^2$ + 6x – 24

⇒$x^2$ – 10x = 0⇒x = 0, 10

Answer: (a)

One day's work of first son = $1/6$

One day's work of second son = $1/{12}$

∴ One day's work of them working together

= $1/6 + 1/{12} = {2 + 1}/{12} = 1/4$

father will finish the work in 4 days.

Answer: (b)

Let the man's upstream speed be $S_u$ kmph and downstream speed be $S_d$ kmph.

Then, Distance covered upstream in 8 hrs 48 min.

d = Distance covered downstream in 4 hrs.

⇒$(S_u × 8 4/5) = (S_d × 4)⇒{44}/5 S_u = 4S_d⇒S_d = {11}/5 S_u$

∴ Required ratio

= $({S_d + S_u}/2) : ({S_d - S_u}/2) = ({16S_u}/5 × 1/2) : ({6S_u}/5 × 1/2) = {8/5} : {3/5}$

= 8 : 3.

Answer: (c)

Let the remaining food will last for x days.

500 men had provision for (27 – 3) = 24 days.

(500 + 300) men had provisions for x days.

More men, Less days (Indirect Proportion)

∴ 800 : 500 :: 24 : x = (800 × x) = (500 × 24)

⇔x=$({500 × 24}/{800})$ = 15

Answer: (c)

$M_1 = 45, D_1 = 18$

Here, $M_2 = x, D_2 = 15$

By the formula, $M_1D_1 = M_2D_2$

∴ $M_2 = {M_1D_1}/{D_2}$

⇒x = ${45 × 18}/{15}$ = 3 × 18 = 54