**Q1. A sum of money is sufficient to pay A’s wages for 21 days and B’s wages for 28 days. The same money is sufficient to pay the wages of both for:**

(a) 12 days

(b) 12 1/4 days

(c) 14 days

(d) 24 1/2 days

**Q2. A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?**

(a) 18 days

(b) 24 days

(c) 30 days

(d) 36 days

**Q3. A and B together can do a piece of work in 12 days, which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C finishes it in 13 days. In how many days C alone will do the work?**

(a) 16

(b) 24

(c) 36

(d) 48

**Q4. A, B and C can do a piece of work in 36, 54 and 72 days respectively. They started the work but A left 8 days before the completion of the work while B left 12 days before the completion. The number of days for which C worked is:**

(a) 4

(b) 8

(c) 12

(d) 24

**Q5. 10 men can complete a piece of work in 15 days and 15 women can complete the same work in 12 days. If all the 10 men and 15 women work together, in how many days will the work get completed?**

(a) 6

(b) 61/3

(c) 62/3

(d) 72/3

**Q6. A, B, C along completed a piece of work in 30, 50 and 40 days. The ratio of the salary of each day is 4 : 3 : 2 respectively. If the total income of A is Rs. 144. Find total income of B.**

(a) Rs. 180

(b) Rs. 185

(c) Rs. 190

(d) Rs. 195

**Q7. A sum of Rs. 3115 is divided among A, B and C such that if Rs. 25, Rs. 28 and Rs. 52 be diminished from their shares respectively, the remainder shares shall be in the ratio of 8 : 15 : 20. Find the share of each.**

(a) Rs. 585, Rs. 1078, Rs. 1452

(b) Rs. 685, Rs. 1178, Rs. 1252

(c) Rs. 485, Rs. 1088, Rs.1352

(d) Rs. 785, Rs. 1378, Rs. 1652

**Q8. A, B and C are partners in a business. A, whose money has been used for 4 months, claims 1/8 of the profit, B whose money has been used for 6 months, claims 1/3 of the profit. C had invested Rs. 1560 for 8 months. How much did A and B contribute?**

(a) Rs. 740, Rs. 1250

(b) Rs. 730, Rs. 1240

(c) Rs. 720, Rs. 1280

(d) Rs. 750, Rs. 1260

**Q9. The sum of ages of a mother and her daughter is 50 years. Also 5 years ago, the mother’s age was 7 times the age of the daughter. What are the present ages of the mother and the daughter?**

(a) 40 years, 10 years

(b) 48 years, 12 years

(c) 32 years, 8 years

(d) 36 years, 9 years

**Q10. The age of Sonal and Nitya are in the ratio of 9 : 5 respectively. After 8 years the ratio of their ages will be 13 : 9. What is the difference in years between their ages?**

(a) 4 years

(b) 12 years

(c) 8 years

(d) 14 years

**Solutions**

S1. Ans.(a)

Sol. Let total money be Rs. x.

A’s 1 day’s wages = Rs. x/21, B’s 1 day’s wages = Rs. x/28.

∴ (A + B)’s 1 day’s wages = Rs. (x/21)+(x/28) = Rs. (x/12)

∴ Money is sufficient to pay the wages of both for 12 days.

S2. Ans.(a)

Sol. 2 (A + B + C)’s 1 day’s work = (1/30)+(1/24)+(1/20)=15/120=(1/8)

⇒ (A + B + C)’s 1 day’s work = 1/16.

Work done by A, B and C in 10 days = 10/16=5/8. Remaining work = (1-(5/8))=3/8.

A’s 1 day’s work = (1/16)-(1/24)=1/48.

Now, 1/48 work is done by A in 1 day.

So, 3/8 work will be done by A in (48×(3/8)) = 18 days.

S3. Ans.(b)

Sol. A’s 5 days’ work + B’s 7 days’ work + C’s 13 days’ work = 1

⇒ (A + B)’s 5 days’ work + (B + C)’s 2 days’ work + C’s 11 days’ work = 1

⇒ 5/12+2/16 + C’s 11 days’ work = 1

⇒ C’s 11 days’ work = 1-(5/12 + 2/16)=11/24.

⇒ C’s 1 day’s work = (11/24 × 1/11)=1/24.

∴ C alone can finish the work in 24 days.

S4. Ans.(d)

Sol. Suppose the work was finished in x days.

The, A’s (x – 8) days’ work + B’s (x – 12) day’s work + C’s x days’ work = 1

⇒ (x – 8)/36 + (x – 12)/54 + x/72 = 1 ⇔ 6 (x – 8) + 4 (x – 12) + 3x = 216

∴ 13x = 312 or x = 24.

S5. Ans.(c)

Sol. 10 men’s 1 day’s work = 1/15; 15 women’s 1 day’s work = 1/12.

(10 men + 15 women)’s 1 day’s work = (1/15) + (1/12)=9/60=3/20.

∴ 10 men and 15 women will complete the work in 3/20=6 2/3 days.

S6. Ans.(a)

Sol.

A B C

Days of working = 30 : 50 : 40

Each day salary = 4 : 3 : 2

Total income = 120 : 150 : 80

12 : 15 : 8

Income of B = 12 × 15 = 180

S7. Ans.(a)

Sol. The total sum after deduction

= 3115 – (25 + 28 + 52) = Rs. 3010

Their diminished share in the ratio 8 : 15 : 20

∴ A’s diminished share =8/43 × 3010

= 8 × 70 = Rs. 560

B’s diminished share =15/43 × 3010

= 15 × 70 = Rs. 1050

C’s diminished share =20/43 × 3010

= 20 × 70 = Rs. 1400

∴ A’s share = 560 + 25 = Rs. 585

B’s share = 1050 + 28 = Rs. 1078

C’s share = 1400 + 52 = Rs. 1452

S8. Ans.(c)

Sol. C’s share =1-(1/8 + 1/3)=13/24

C’s investment = 1560 × 8

If 13/24=1560×8

Then, 1/8=(1 ×1560 ×8 ×24)/(8 ×13)

= 120 × 24

A’s share is for 4 months

∴ 120 × 24 = 120 × 6 × 4

A’s share = 120 × 6 = 720

B’s share =1/3=(1 ×1560 × 8 × 24)/(3 ×13)

= 120 × 8 × 8

B’s share is for 6 months

120 × 8 × 8 = 20 × 6 × 8 × 8

B’s share = 20 × 8 × 8 = 1280

S9. Ans.(a)

Sol. Let 5 years ago, ages of mother and her daughter were ‘7x’ years and ‘x’ years respectively.

∴ Present age of mother = (7x + 5) years

And present age of her daughter = (x + 5) years

According to question

Sum of their present age = 50

⇒ (7x + 5) + (x + 5) = 50

⇒ 8x + 10 = 50

⇒ 8x = 40

⇒ x = 5

∴ Present age of mother

= 7x + 5 = 7 × 5 + 5 = 35 + 5 = 40 years

and present age of her daughter

= x + 5 = 5 + 5 = 10 years.

S10. Ans.(c)

Sol. Let the ages of Sonal and Nitya be ‘9x’ the year ‘5x’ years respectively.

After 8 years,

Age of Sonal = (9x + 8) years

And age of Nitya = (5x + 8) years

According to question

(9x + 8)/(5x + 8)=13/9

⇒ (9x + 8) × 9 = (5x + 8) × 13

⇒ 81x + 72 = 65x + 104

⇒ 81x – 65x= 104 – 72

⇒ 16x = 32

⇒ x = 2

Difference of their ages

= 9x – 5x = 4x = 4 × 2 = 8 years.