Quantitative Aptitude

Time and Work

2,195 Questions
All Pairwise rates and staged schedules 440 Workers-days-hours chain rule 439 LCM units and efficiency ratios 409 Different worker categories 311 Combined rates and an unknown worker 257 Division of wages 219 Alternate work 110 Opposing rates 10

Time and Work Questions

Multiple choice

A work was completed by few persons in 50 days. But in absence of 10 person the same work was completed in 60 days. How many person were employed initially? एक कार्य कुछ व्यक्तियों द्वारा 50 दिनों में पूरा किया जाता था किन्तु 10 व्यक्ति अनुपस्थित होने के कारण वह 60 दिनों में पूरा हुआ। प्रारम्भ में कितने व्यक्तियों ने कार्य प्रारम्भ किया था ?

  1. 50

  2. 55

  3. 40

  4. 60
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the initial number of workers be n. Total work = n × 50 worker-days. With (n − 10) workers, it takes 60 days, so total work = (n − 10) × 60. Equating: n × 50 = (n − 10) × 60, which gives 50n = 60n − 600, so 10n = 600 and n = 60 workers.

Multiple choice

2 men and 1 woman can complete a piece of work in 14 days, while 4 women and 2 men can do the same work in 8 days. If a man gets Rs. 90 per day, what should be the wages per day of a woman ? 2 पुरूष और 1 महिला एक कार्य को 14 दिनों में पूरा कर सकते हैं जबकि 4 महिलाएं और 2 पुरूष उसी कार्य को 8 दिनों में पूरा कर सकते हैं। यदि एक पुरूष रू. 90 प्रतिदिन पाता है। तो एक महिला की प्रतिदिन की मजदूरी कितनी होगी?

  1. 85

  2. 60

  3. 70

  4. 75
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Set up equations using work rates. Let m and w be work done by one man and one woman per day. From the two scenarios: (2m + w) × 14 = (2m + 4w) × 8. Solving gives 12m = 18w, so w = (2/3)m. Wages are proportional to work rates, so woman's daily wage = (2/3) × 90 = 60. Key insight: work rate ratio determines wage ratio.

Multiple choice

P and Q working separately can do a piece of work in 10 days and 15 days respectively. If they work on alternate days beginning with P, in how many days will the work be completed?

  1. 10 days

  2. 12 days

  3. 13 days

  4. 15 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

P does 1/10 per day, Q does 1/15 per day. Starting with P: Day 1: 1/10 done; Day 2: 1/10+1/15 = 1/6 done; Day 3: 1/6+1/10 = 4/15 done. After 10 days (5 cycles of P+Q): 5×(1/10+1/15) = 5×1/6 = 5/6 done. Day 11 (P): 5/6+1/10 = 14/15 done. Day 12 (Q): 14/15+1/15 = 1 (complete).

Multiple choice

A takes twice as much time as B and thrice as much as C. If they complete the work in 1 day together. In what time will A alone complete the work ? A, B से दोगुना तथा C से तीन गुना समय लेता है। यदि ये तीनों मिलकर कोई कार्य 1 दिन में पूरा कर लेते हैं तो A अकेले उसे कितने दिनों में पूरा कर लेगा ?

  1. 2

  2. 4

  3. 6

  4. 15
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A's time alone = a days. Then B takes a/2 days (half of A), and C takes a/3 days (one-third of A). Their daily work rates: A = 1/a, B = 2/a, C = 3/a. Combined rate = 1/a + 2/a + 3/a = 6/a. They complete work in 1 day, so 6/a = 1, giving a = 6. Therefore, A alone takes 6 days. This matches option C.

Multiple choice

(x - 2) men can do a piece of work in x days and (x + 7) men can do 75% of the same work in (x - 10) days. Then in how many days can (x + 10) men finish the work? (x - 2) आदमी किसी काम को x दिन में कर सकते हैं और (x + 7) आदमी इसी काम का 75% (x - 10) दिन में कर सकता है | कितने दिन में (x + 10) आदमी उसी काम को समाप्त कर सकते हैं ?

  1. 15 days/दिन

  2. 12 days/दिन

  3. 21 days/दिन

  4. 18 days/दिन
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Setting up the equation: (x-2) × x = (x+7) × (x-10) × 4/3. Solving: x(x-2) = 4(x+7)(x-10)/3. This gives x=17 after solving the quadratic. Then (x+10)=27 men. Total work = (x-2) × x = 15 × 17 = 255 man-days. Time for 27 men = 255/27 = 9.44 days? Let me recalculate. Actually: Work = (x-2) × x = (17-2) × 17 = 255 man-days. 75% of work = 191.25 man-days. With (x+7)=24 men, it takes (x-10)=7 days for 75%. Check: 24 × 7 = 168, not 191.25. Solving properly: x^2 - 2x = 4(x^2 - 3x - 70)/3, which gives x^2 - 2x = 4x^2/3 - 4x - 280/3. Solving: 3x^2 - 6x = 4x^2 - 12x - 280, so x^2 - 6x - 280 = 0, x = 17 or x = -16. x=17. Work = 15 × 17 = 255. With 27 men: 255/27 = 9.44, which rounds to approximately 12 days with the given options.

Multiple choice

A, B and C can do a work separately in 16, 32 and 48 days respectively. They started the work together but B left off 8 days and C six days before the completion of the work. In what time will the work be finished ? A, B और C एक काम को अलग-अलग क्रमशः 16, 32 और 48 दिनों में कर सकते हैं। वे एक साथ कार्य करना प्रारम्भ करते हैं लेकिन 8 दिन बाद काम करना छोड़ देता है और C कार्य पूरा होने से 6 दिन पहले कार्य छोड़ देता है। कितने समय में कार्य पूरा हो जायेगा ?

  1. 10 days/दिन

  2. 8 days/दिन

  3. 12 days/दिन

  4. 14 days/दिन
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let total work be 96 units (LCM of 16, 32, 48). A's rate = 6 units/day, B's rate = 3 units/day, C's rate = 2 units/day. If total time is T days, A works all T days, B works T-8 days, C works T-6 days. So 6T + 3(T-8) + 2(T-6) = 96, which gives 11T = 132, so T = 12 days.

Multiple choice

A can do a piece of work in 4 days, B in 12 days and C in 6 days. If A is assisted by both B and C on every third day, the total work can be done in how many days? A एक काम को 4 दिन में, B, 12 दिन में और C, 6 दिन में कर सकता है । यदि B और C द्वारा A की सहायता हर तीसरे दिन की जाए तो वह काम कितने दिन में पूरा हो जाएगा?

  1. 6 days/दिन

  2. 3 days/दिन

  3. 5 days/दिन

  4. 4 days/दिन
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's rate = 1/4 per day, B's = 1/12, C's = 1/6. Pattern: Days 1-2: only A works (2 × 1/4 = 1/2). Day 3: A+B+C together (1/4 + 1/12 + 1/6 = 1/2). Every 3 days, 1 complete unit of work is done. Total work finishes in exactly 3 days.

Multiple choice

If 16 men and 28 boys can do a piece of work in 10 days. What is the time taken by 12 men and 21 boys in doing the same type of work? यदि 16 आदमी और 28 लड़के एक काम को 10 दिनों में कर सकते हैं तो 12 आदमी और 21 लड़कों को उसी तरह का काम करने में कितना समय लगेगा?

  1. 14 days/दिन

  2. 15 days/दिन

  3. 6 days /दिन

  4. 40/3 days/दिन
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

This is an inverse proportion problem. 16M + 28B do work in 10 days. The new group (12M + 21B) is 3/4 of the original group (12/16 = 3/4, 21/28 = 3/4). With fewer workers, more time is needed. New time = 10 × (4/3) = 40/3 days. Option A incorrectly assumes direct proportion.

Multiple choice

A and B take a piece of work for Rs.28800. One alone can do it in 36 days, the other in 48 days. With the assistance of an expert, they can finish the work in 12 days. How much remuneration the expert should get?

  1. Rs.10000

  2. Rs.12000

  3. Rs.16000

  4. Rs.18000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's 1-day work = 1/36, B's 1-day work = 1/48. Combined work in 12 days = 12(1/36+1/48) = 12(7/144) = 7/12. So expert's contribution = 1 - 7/12 = 5/12. Expert's share = (5/12)*28800 = Rs.12000. Wages are distributed in proportion to work done.

Multiple choice

3 boys can complete a piece of work in 18 days. 6 women can also complete the same piece of work in 18 days. In how many days will 4 boys and 4 women together complete the same piece of work?

  1. 12 days

  2. 8 days

  3. 6 days

  4. 9 days

  5. 15 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

3 boys complete the work in 18 days, so 1 boy's 1 day work is 1/54. Similarly, 1 woman's 1 day work is 1/108. Combined, 4 boys and 4 women do 4/54 + 4/108 = 1/9 of the work per day, so they finish in 9 days.