Practice Efficiency of the worker - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) A can do a work in 5 days less than the time taken by B to do it. If both of them together take11$1/9$ days, then the time taken by ‘B’ alone to do the same work (in days) is
(a)
(b)
(c)
(d)
Using Rule 2,
If the time taken by B to complete the work be x days,
then time taken by A = (x - 5) days
$1/x + 1/{x - 5} = 9/100$
⇒ ${x - 5 + x}/{x(x - 5)} = 9/100$
⇒ $9x^2 - 45x = 200x –500$
⇒ $9x^2 - 245x + 500 = 0$
⇒ $9x^2 - 225x - 20x + 500 = 0$
⇒ $9x (x - 25) - 20 (x - 25)$ = 0
⇒ $(x - 25) (9x - 20)$ = 0
⇒ $x = 25$ because $x ≠ 20/9$
Q-2) Shashi can do a piece of work in 20 days. Tanya is 25% more efficient than Shashi. The number of days taken by Tanya to do the same piece of work is :
(a)
(b)
(c)
(d)
Time taken by Shashi in doing 1 work = 20 days
Tanya is 25% more efficient than Shashi.
Time taken by Tanya
= $100/125 × 20$ = 16 days
Q-3) A works twice as fast as B. If B can complete a piece of work independently in 12 days, then what will be the number of days taken by A and B together to finish the work?
(a)
(b)
(c)
(d)
A is twice efficient than B.
Time taken by B = 12 days
Time taken by A = 6 days
(A + B)’s 1 day’s work
= $1/6 + 1/12 = {2 + 1}/12 = 1/4$
∴ Required time = 4 days
Q-4) 5 men and 2 women working together can do four times as much work per hour as a man and a woman together. The work done by a man and a woman should be in the ratio :
(a)
(b)
(c)
(d)
5m + 2w = 4m + 4w ⇒ m = 2w
Required ratio = 2 : 1
Q-5) A can do a work in 9 days, if B is 50% more efficient than A, then in how many days can B do the same work?
(a)
(b)
(c)
(d)
Time taken by B = $9 × 100/150$ = 6 days
Using Rule 17,
Here, x = 9, R = 50%
Time taken by B = $x × 100/{100 + R}$ days
= $9 × 100/150$ = 6 days
Q-6) A 10 hectare field is reaped by 2 men, 3 women and 4 children together in 10 days. If working capabilities of a man, a woman and a child are in the ratio 5 : 4 : 2, then a 16 hectare field will be reaped by 6 men,4 women and 7 children in
(a)
(b)
(c)
(d)
Using Rule 1,
Ratio of the working capabilities of a man, a woman and a child = 5 : 4 : 2
Ratio of man, woman and child equivalence = $1/5 : 1/4 : 1/2$
= $1/5 × 20 : 1/4 × 20 : 1/2 × 20$ = 4 : 5 : 10
or 4 men ≡ 5 women ≡ 10 children
4 men = 10 children
2 men ≡ 5 children and 6 men ≡ 15 children
5 women = 10 children
3 women ≡ 6 children
4 women ≡ 8 children
2 men + 3 women + 4 Children = 15 children
6 men + 4 women + 7 children = 30 children
| Children | Field | Days |
| 15 | 10 | 10 |
| ↑ | ↓ | ↓ |
| 30 | 16 | x |
∴ ${30 : 15}/{10 : 16}]$ : : 10 : x
where, x is no. of days
30 × 10 × x = 15 × 16 × 10
x = ${15 × 16 × 10}/{30 × 10} = 8$ days
Q-7) A can do a certain job in 12 days. B is 60% more efficient than A. To do the same job B alone would take :
(a)
(b)
(c)
(d)
Time taken by B
= $12 × 100/160 = 15/2 = 7{1}/2$ days
Using Rule 17,
Here, x = 12, R = 60%
Time taken by B = $x × 100/{100 + R}$ days
= $12 × 100/160$ days
= $15/2$ days = 7$1/2$ days
Q-8) A man does double the work done by a boy in the same time. The number of days that 3 men and 4 boys will take to finish a work which can be done by 10 men in 8 days is
(a)
(b)
(c)
(d)
According to the question,
1 man ≡ 2 boys
3 men + 4 boys ≡ (3 + 2) men ≡ 5 men
$M_1D_1 = M_2D_2$
5 × $D_1$ = 10 × 8
$D_1 = {10 × 8}/5$ = 16 days
Q-9) A is 50% as efficient as B. C does half of the work done by A and B together. If C alone does the work in 20 days, then A, B and C together can do the work in
(a)
(b)
(c)
(d)
If B alone completes the work in x days, A will do the same in 2x days.
(A + B)’s 1 day’s work = $1/x + 1/{2x} = {2 + 1}/{2x} = 3/{2x}$
and C’s 1 day’s work = $3/{4x}$
$3/{4x} = 1/20$
4x = 3 × 20
$x = {3 × 20}/4 = 15$
(A + B + C)’s 1day’s work
= $1/{2x} + 1/x + 3/{4x} = 1/30 + 1/15 + 1/20$
= ${2 + 4 + 3}/60 = 9/60 = 3/20$
Hence, all three together will complete the work in
$20/3$ or $6{2}/3$ days.
Q-10) A takes twice as much time as B and thrice as much as C to complete a piece of work. They together complete the work in1 day. In what time, will A alone complete the work.
(a)
(b)
(c)
(d)
Let time taken by C to complete the work = x days
Time taken by A to complete the work = 3x days
and time taken by B to complete the work = ${3x}/2$ days
According to the question,
$1/{3x} + 1/{{3x}/2} + 1/x = 1$
$1/{3x} + 2/{3x} + 1/x = 1$
${1 + 2 + 3}/{3x} = 1$
$6/{3x} = 1 ⇒ 2/x = 1 ⇒ x = 2$
Time taken by A
= 3x = 3 × 2 = 6 days