time and work Model Questions & Answers, Practice Test for ssc cgl tier 1 2023

Answer: (d)

Let if both A and B work together, they take x days.

∴ (A + B)'s days's work = $1/x$ th work

A's 1 day's work = $1/{x + 8}$ th work

's 1 day's work = $1/{x + 9/2}$ th work.

Now, $1/{x + 8} + 2/{2x + 9} = 1/x$

⇒ x(2x + 9 + 2x + 16) = (x + 8)(2x + 9)

⇒ $4x^2 + 25x = 2x^2 + 25x + 72$

$x^2$ = 36⇒x = 6 days

Alternate Method :-

A and B together finish the work in $(√ {8 × 9/2})$ = 6 days

Answer: (c)

If new speed is $a/b$ of original speed, then

usual time × $(b/a - 1)$ change in time

&there4 usual time × $(4/3 - 1) = 1/3$

⇒ usual time = $1/3$ × 3 = 1 hr

Answer: (c)

Distance covered by a bus in 4 hours = 160 km.

∴ Distance covered by a bus in 1 hour = ${160}/4$ = 40 km

Further, Distance covered by a train in 5 hours = 320 km

∴ Distance covered by a train in 1 hour = ${320}/5$ = 64 km

Required ratio = ${40}/{64} = 5/8$ = 5 : 8

Answer: (c)

Work done by (A + B) in 1 day = $1/{12}$

Work done by (B + C) in 1 day = $1/{16}$

Let C finishes the work in x days.

Then, work done by C in 1 day = $1/x$

We have, A's 5 days' work + B's 7days' work + C's 13 days' work = 1

or [(A + B)'s 5 days' + (B + C)' s 2 days' + C's 11 days'] work = 1

or $5/{12} + 2/{16} + {11}/x$ = 1 or x = 24 days

Answer: (b)

Units of work done by A in 1 day = $1/9$

Units of work done by B in 1 day = ${15}/{90}$ = $1/6$

Hence, B alone will complete the work in 6 days.