1. Rs 1087 was divided among A, B, and C. Such that if Rs. 10, 13 and 14 be diminished form their shares respectively, the remainders will be in the ratio of 3 : 5 : 7. What is the share of A?

(1) Rs. 220

(2) Rs. 210

(3) Rs. 310

(4) Rs. 320

### Show Answer

**Explanation :**

**(1) Sum of money to be divided**

**= Rs. 1087**

**Total money to be withdrawn**

**= Rs (10 + 13 + 14) = Rs. 37**

**Remainder = Rs. (1087 – 37)**

**= Rs. 1050**

**If is to be divided in the ratio**

**3 : 5 : 7**

**Therefore Share of A**

**= Rs. (210 + 10) = Rs. 220**

2. A can do a piece of work in 6 days. B takes 8 days and C takes as long as A and B and C working together will complete the work in :

(1) 2 2 / 5 days

(2) 2 2 / 11 days

(3) 3 3 / 7 days

(4) 3 2 / 5 days

### Show Answer

**Explanation :**

**(1) (A + B)S 1 day’s work**

**= 1 / 6 + 1 / 8 = 7 / 24**

**Therefore (B + C)’s 1 day’s work**

**= 1 / 8 + 7 / 24 = 5 / 12**

**Therefore B and C together will complete the work in**

**12 / 5 = 2 2 / 5 days**

3. A cistern is normally filled in 8 hours but takes 2 hours longer to be filled because of a leak in the bottom. If the cistern id full the leak will empty in :

(1) 20 hrs

(2) 36 hrs

(3) 40 hrs

(4) None f these

### Show Answer

**Explanation :**

**(3) Let leak cn empty the full tank in x hours.**

**1 / 8 – 1 / x = 1 / 10**

**Therefore 1 / x = 1 / 8 – 1 / 10 = 1 / 40**

**Therefore x = 40**

4. A person sets to cover a distance of 12 km in 45 minutes, If the covers 3 / 4 of the distance in 2 / 3 rd time. What should be his speed to cover the remaining distance in the remaining time?

(1) 16 km/hr

(2) 18 km/hr

(3) 12 km/hr

(4) 14 km/hr

### Show Answer

**Explanation :**

**(3) Distance already covered**

**= 3 / 4 * 12 = 9 km**

**Time spent = 2 / 3 * 45 min.**

**= 30 min.**

**Distance left = (12 – 9) km**

**= 3 km**

**Time left = (45 – 30) min**

**= 15 min.**

**Therefore Reqd. speed**

**= 3 / 15 / 60 km/hr. = 12 km/hr.**

5. The diameter of a circle is 105 cm, less than the circumference. What is the diameter of the circle?

(1) 42 cm

(2) 44 cm

(3) 48 cm

(4) 49 cm

### Show Answer

**Explanation :**

**(4) Let radius = r**

**2 pie r – 2r = 105**

**Therefore 2 r = 105 / pie – 1 = 105 / 22 / 7 – 1 = 49**

6. A and B enter into a partnership by making investments in the ratio 1 : 2, 5% of the total profit goes to chairty. If B’s share is Rs 760 total profit is :

(1) Rs. 1200

(2) Rs. 1800

(3) Rs. 2400

(4) Rs. 1560

### Show Answer

**Explanation :**

**(1) Let Rs x be the total profit.**

**Profit available for distribution among A and B = 9.5x This is to be distributed in the ratio = 1 : 2**

**Therefore 2 / 3 * 0.95 * = 760**

**= x = 1200**

7. The simple interest on a sum of money is 1 / 9 of the principal and the number of years is equal to the rate percent per annum. The rate percent per annum is :

(1) 100 / 9 %

(2) 10 / 3 %

(3) 5 / 3 %

(4) None of the these

### Show Answer

**Explanation :**

**(2) Let Principal = Rs x and rate**

**= r % Then interest**

**= 1 / 9 x and no. of years**

**= r Therefore x / 9 = x * r * r / 100**

**Therefore r^2 = 100 / 9 = r = 10 / 3**

8. A motorboat can row 25 km up stream and 39 km downstream in 8 hours. Also it can go 35 km upstream and 52 km downstream in 11 hours. The rate (in km/hr) of flow is :

(1) 5

(2) 4

(3) 8

(4) 6

### Show Answer

**Explanation :**

**(2) Let rate upstream**

**= x km/hr.**

**and rate down stream**

**= y km/hr.**

**Then 25 / x + 39 / y = 8… (I)**

**and 35 / x + 52 / y = 11… (II)**

**Multiplying (I) by 7 and (II) by 5**

**and subtracting 13 / y = 56 – 55**

**Therefore y = 13**

**Therefore (I) = 25 / X = 8 – 3 = 5**

**Therefore x = 5**

**Therefore Rate of flow = 1 / 2**

**(13 – 5) = 4km/hr.**

9. At an election where there are two candidates only. the candidate who gets 43% of the votes is rejected by a margin of 420 votes. The total number of votes polled were :

(1) 3000

(2) 3500

(3) 2500

(4) 2800

### Show Answer

**Explanation :**

**(1) Let no. of votes polled = xNO.**

**of votes of lossing candidate**

**= 0.43 x**

**No. of votes of winning candidate**

**= x – 0.43 x**

**= 0.57 x**

**Therefore 0.57 x – 0.43 x = 420**

**0.14 x = 420**

**x = 3000**

10. A can do a work in 6 days and B in 9 days. How many days will both take together to complete the work?

(1) 7.5

(2) 5.4

(3) 3.6

(4) 3

### Show Answer

**Explanation :**

**(3) According to question,**

**A can finsih the whole work in 6 days.**

**Therefore A’s one day’s work = 1 / 6**

**Similarly,**

**B’s one day’s work = 1 / 9**

**(A + B)’s one day’s work**

**= (1 / 6 + 1 / 9) = (3 + 2 / 18) = 5 / 18**

**Therefore, (A + B)’s can finish the**

**whole work in 18 / 5 days i.e. 3.6 days**