**Q1. A, B, C enters into a partnership with shares in the ratio 7/2:4/3:6/5. After 4 months, A increases his share by 50%. If the total profit at the end of one year be Rs. 21600, then B’s share in the profit is:**

(a) Rs. 2100

(b) Rs. 2400

(c) Rs. 3600

(d) Rs. 4000

**Q2. Two partners invested Rs. 12500 and Rs. 8500 in a business, They decided that 60% of the profit incurred from the business will be equally divided between them while remaining profit will be assumed as interest on their capitals. If one of the partners receives Rs. 300 more profit than the other, what is the total profit in the business?**

(a) Rs. 3937.50

(b) Rs. 4940.50

(c) Rs. 3936.50

(d) Rs. 4156

**Q3. A, B and C starts a business. If the ratio of their periods of investment are 2:3:6 and their profits are in the ratio of 4:5:6, then the ratio of capitals of A, B and C is:**

(a) 6:8:10

(b) 12:10:6

(c) 10:12:6

(d) None of these

**Q4. A, B and C rented a pasture. A puts in 12 oxen for 6 months, B put 8 oxen for 7 months and C put 6 oxen for 8 months. If the rent of the field is Rs. 396, what amount of rent was paid by A?**

(a) Rs. 126

(b) Rs. 108

(c) Rs. 162

(d) Rs. 168

**Q5. A, B, C and D enters into partnership. A contributes 1/3 of the capital, B contributes 1/4, C contributes 1/5 and D contributes the rest. What is the share of D when profit is Rs. 6000?**

(a) Rs. 2000

(b) Rs. 1600

(c) Rs. 1200

(d) Rs. 1300

**Q6. In a group of 50 people, 35 speak Hindi, 25 speak both Hindi and English and all the people speak Hindi or English or both. The number of people who speak English only is:**

(a) 40

(b) 20

(c) 15

(d) 10

**Q7. A playground has the shape of a rectangle with two semi-circles on its smaller sides as diameters, added outside. If the sides of the rectangle are 36 m and 24.5 m, then the area of the playground is:**

(use π=22/7)

(a) 2259.529 m^2

(b) 1353.625 m^2

(c) 1139.523 m^2

(d) None of these

**Q8. The length of a rectangle is twice the diameter of a circle. The circumference of the circle is equal to the area of a square of side 22 cm. What is the breadth of the rectangle if its perimeter is 668 cm?**

(a) 24 cm

(b) 26 cm

(c) 52 cm

(d) Cannot be determined

**Q9. The sum of the areas of the 10 squares, the lengths of whose sides are 20 cm, 21cm, …, 29 cm respectively is:**

(a) 6085 cm^2

(b) 8555 cm^2

(c) 2470 cm^2

(d) 11025 cm^2

**Q10. The number of coins of radius 0.75 cm and thickness 0.2 cm to be melted to make a right circular cylinder of height 8 cm and base radius 3 cm is:**

(a) 640

(b) 460

(c) 500

(d) 600

**Solutions**

S1. Ans.(d)

Sol. The given ratio = 7/2:4/3:6/5 = 105:40:36

Let they initially invest Rs. 105, Rs. 40 and Rs. 36, respectively.

Ratio of investments

= [105 × 4 + (150% of 105) × 8]: (40 × 12): (36 × 12)

= 1680:480:432 = 35:10:9

B’s share = Rs. (21600×(10/54)) = Rs. 4000.

S2. Ans.(a)

Sol. Suppose, total profit in the business = Rs. x

∴ 60% of total profit = 60% of x = Rs. 3x/5

∴ The two partners will receive profit of Rs. 3x/10 and Rs. 3x/10, respectively.

∴ Remaining profit = x-(3x/5)=Rs.2x/5.

The remaining profit assumed as interest on the capital will be divided

in the proportion of their capitals.

Their capital ratio = 12500:8500 = 25:17

Sum of proportional = 25 + 17 = 42

∴ The first partner’s profit = (25/42)×(2x/5)=Rs.5x/21

The second partner’s profit = (17/42)×(2x/5)=Rs.17x/105

Given (3x/10)+(5x/21)=(3x/10)+(17x/105)+300

∴(8x/105)=300

or, x=(105 × 300)/8=Rs.3937.50.

∴ Total profit in the business = Rs. 3937.50.

S3. Ans.(b)

Sol. We have, P1:P2:P3 = 4:5:6 and t1:t2:t3 = 2:3:6.

∴ Required ratio = P1/t1∶P2/t2∶P3/t3 =4/2:5/3:6/6

or, 12:10:6.

Thus, A, B and C invested their capitals in the ratio of 12:10:6.

S4. Ans.(c)

Sol. Ratio in which A, B, C pays the rent

= (6 × 12): (8 × 7): (6 × 8)

= 72:56:48

= 9:7:6

Rent paid by A = 9/22 × Rs. 396 = Rs. 162.

S5. Ans.(d)

Sol. D’s capital = 1-(1/3)-(1/4)-(1/5)=13/60

Profit ratio of A, B, C, D = 1/3:1/4:1/5:13/60

⇒ 20:15:12:13

∴ Share of D = 13/60 × Rs. 6000 = Rs. 1300.

S6. Ans.(c)

Sol. Number of people speak English only

= 50 – (10 + 25)

= 15

S7. Ans.(b)

Sol. Area = 24.5 × 36 + π×(24.5/2)^2

= 1353.625 m^2

S8. Ans.(b)

Sol. 2(l + b) = 668

∴ l + b = 334

∴ l = (334 – b)

Length of a rectangle = Twice the diameter of a circle

334 – b = 2 × d = 2 × 2r = 4r

∴ r = (334 – b)/4

Area of square = Circumference of circle

(22)^2=2πr

484=(2×22(334-b))/(7×4)

∴ 334 – b = (484 × 7 × 4)/(2 × 22) = 308

∴ b = 334 – 308 = 26 cm

S9. Ans.(a)

Sol. required sum (20)^2+⋯+(29)^2

=((1)^2+⋯+(29)^2 )-(1^2+⋯+(19)^2 )

=(29(29+1)(2×29+1)/6)-(19(19+1)(2×19+1)/6)

=((29×30×59)/6)-((19×20×39)/6)

= 8555 – 2470 = 6085 cm^2

S10. Ans.(a)

Sol. (π × (3)^2 × 8)/(π(0.75)^2 × 0.2) = 640.