time and work Model Questions & Answers, Practice Test for ibps so prelims 2023

Answer: (a)

27 men mow 225 hectares in15 days

∴ 1 man mow 225 hectares in (15 × 27) days (indirect)

∴ 1 man mow 1 hectares in 15 ${15×27}/{255}$ days (direct)

1 man mow 165 hectares in ${15×27}/{255}$ ×165 days (direct)

∴ 33 men mow 165 hectares in${15×27×165}/{225×33}$= 9 days

Answer: (b)

Speed with the stream = 10.56 km. an hour.

Speed against the stream = ${352}/4 × {60}/{1000}$ = 5.28 = an hour

⇒Speed in still water = $1/2$ (10.56 + 5.28) = 7.92 kmph

Answer: (a)

Ratio of time taken by A and B = 160 : 100

= 8 : 5

Suppose, B alone takes x days to do the job then, 8 : 5 : : 12 : x

8x = 5 × 12

x = ${5×12}/8=7 1/2$ days.

Answer: (c)

Let average speed of train be x km/hr.

${225}/x + {245}/{x + 8} = 5$

${45}/x + {49}/{x + 8}$ = 1

45x + 360 + 49x = $x^2$ + 8x

$x^2$ + 86x - 360 = 0

$x^2$ - 90x + 4x - 360 = 0

x(x - 90) + 4(x - 90) = 0

(x - 90)(x + 4) = 0

x = 90, -4

Speed cannot be negative.

Therefore average speed of train is 90 km/hr.

Answer: (c)

Let actual speed of train = S m/sec

and length of train = Lm.

Then, $S - {2 × 5}/{18} = L/9$

⇒9S = L + 5 ... (i)

and S - 4 × $5/{18} = L/{10}$

⇒90S = 9L + 100 ... (ii)

By (i) & (ii), we get L = 50 m.