Practice Working with man woman child - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) A man, a woman and a boy can complete a work in 20 days, 30 days and 60 days respectively. How many boys must assist 2 men and 8 women so as to complete the work in 2 days ?
(a)
(b)
(c)
(d)
Part of work done by 2 men and 2 women in 2 days.
= $2(2/20 + 8/30)$
= $2(1/10 + 8/30) = 2({3 + 8}/30)$
= $22/30 = 11/15$
= Remaining work =$1 - 11/15 = 4/15$
Work done by 1 boy in 2 days
= $2/60 = 1/30$
Number of boys required to assist = $4/15 × 30 = 8$
Using Rule 14,
Here, A = 1, B = 1, C = 1
a = 20, b = 30, c = 60
$A_1 = 2, B_1$ = 8
Required time = $1/{A_1/{A × a} + B_1/{B × b} + C_1/{C × c}$
2 = ${1/{2/{1 × 20} + 8/{1 × 30} + x/{1 × 60}$
2 = $10/{2/2 + 8/3 + x/6}$
2 = $10/{{6 + 16 + x}/6}$
22 + x = 30 ⇒ x = 8
∴ Number of boys = 8
Q-2) 18 men or 36 boys working 6 hours a day can plough a field in 24 days. In how many days will 24 men and 24 boys working 9 hours a day plough the same field ?
(a)
(b)
(c)
(d)
18 men ≡ 36 boys ⇒ 1 man ≡ 2 boys
24 men + 24 boys ≡ (24 + 12) men ≡ 36 men
$M_1D_1T_1 = M_2D_2T_2$
$18 × 24 × 6 = 36 × D_2$ × 9
$D_2 = {18 × 24 × 6}/{36 × 9}$ = 8 days
Q-3) A man is twice as fast as a woman and a woman is twice as fast as a boy in doing a work. If all of them, a man, a woman and a boy can finish the work in 7 days, in how many days a boy will do it alone ?
(a)
(b)
(c)
(d)
Using Rule 11,
According to the question,
1 man ≡ 2 women ≡ 4 boys
1 man + 1 woman + 1 boy
= (4 + 2 +1) boys = 7 boys
$M_1D_1 = M_2D_2$
7 × 7 = 1 × $D_2$
∴ $D_2$ = 49 days
Q-4) A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in $1/4$ of a day?
(a)
(b)
(c)
(d)
1 man’s 1 day’s work = $1/3$
1 woman’s 1 day’s work = $1/4$
1 boy’s 1 day’s work = $1/12$
(1 man + 1 woman)’s $1/4$ day’s work = $1/4(1/3 + 1/4) = 7/48$
Remaining work = $1 - 7/48 = 41/48$
Now, 1 boy’s $1/4$ day’s work = $1/4 × 1/12 = 1/48$
$41/48$ work will be done by $41/48$ × 48 = 41 boys.
Q-5) A man, a woman and a boy together finish a piece of work in 6 days. If a man and a woman can do the work in 10 and 24 days respectively. The days taken by a boy to finish the work is
(a)
(b)
(c)
(d)
Time taken by boy = x days
$1/10 + 1/24 + 1/x = 1/6$
$1/x = 1/6 - 1/10 - 1/24$
= ${20 - 12 - 5}/120 = 3/120 = 1/40$
x = 40 days
Using Rule 18,
Here , x = 6, y = 10, z = 24
Number of days = ${xyz}/{yz –x(y + z)}$ days
= ${6 × 10 × 24}/{10 × 24 - 6(10 + 24)}$
= $1440/{240 - 204} = 1440/36$ = 40 days
Q-6) 3 men or 7 women can do a piece of work in 32 days. The number of days required by 7 men and 5 women to do a piece of work twice as large is
(a)
(b)
(c)
(d)
3 men ≡ 7 women
7 men ≡ ${7 × 7}/3 = 49/3$ women
7 men + 5 women = $(49/3 + 5)$ women
= $({49 + 15}/3)$ women = $64/3$ women
${M_1D_1}/W_1 = {M_2D_2}/W_2$
${7 × 32}/1 = {64 × D_2}/{3 × 2}$
$D_2 = {7 × 32 × 3 × 2}/64$ = 21 days
Using Rule 12,
Here, A = 3, B = 7, a = 32
$A_1 = 7, B_1$ = 5
Required time = $a/{A_1/A + B_1/B}$
= $32/{7/3 + 5/7} = 32/64 × 21 = 21/2$
They do the twice work in
$21/2$ × 2 = 21 days
Q-7) If 10 men or 20 boys can make 260 mats in 20 days, then how many mats will be made by 8 men and 4 boys in 20 days?
(a)
(b)
(c)
(d)
10 men ≡ 20 boys ⇒ 1 man ≡ 2 boys
8 men + 4 boys = (16 + 4) boys = 20 boys
Hence, 8 men and 4 boys will make 260 mats in 20 days.
Q-8) Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. The ratio between the capacity of a man and a woman is
(a)
(b)
(c)
(d)
20 women complete 1 work in 16 days.
16 men complete same work in 15 days
16 × 15 men ≡ 20 × 16 women
3 men ≡ 4 women
∴ Required ratio = 4 : 3
Q-9) 12 men and 16 boys can do a piece of work in 5 days; 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is
(a)
(b)
(c)
(d)
Work done by 12 men + 16 boys in 5 days
≡ Work done 13 men + 24 boys in 4 days
(60 men + 80 boys)’s 1 day’s work ≡ (52 men + 96 boys)’s 1 day’s work
(60 - 52) men ≡ (96 - 80) boys
8 men ≡ 16 boys ⇒ 1 man ≡ 2 boys
∴ Required ratio = 2 : 1
Q-10) If 3 men or 4 women can plough a field in 43 days, how long will 7 men and 5 women take to plough it ?
(a)
(b)
(c)
(d)
3 men = 4 women
1 man = $4/3$ women
7 men = ${7 × 4}/3 = 28/3$ women
7 men + 5 women = $28/3 + 5$
= ${28 + 15}/3 = 43/3$ Women
Now, $M_1D_1 = M_2D_2$
4 × 43 = $43/3 × D_2$ ,
where $D_2$ = number of days
$D_2 = {4 × 3 × 43}/43$ = 12 days.
Using Rule 12,
Here, A = 3, B = 4, a = 43, $A_1$ = 7 and $B_1$ = 5
Time taken = ${a(A × B)}/{A_1B + B_1A}$
= ${43(3 × 4)}/{7 × 4 + 5 × 3}$
= ${43 × 12}/43$ = 12 days