**1.**Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:

(a) 4

(b) 5

(c) 6

(d) 8

**2.**It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:

(a) 2 : 3

(b) 3 : 2

(c) 3 : 4

(d) 4 : 3

**3.**A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?

(a) Rs. 35

(b) Rs. 245

(c) Rs. 350

(d) Cannot be determined

**4.**A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs.6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit.

(a) RS. 1900

(b) Rs. 2660

(c) Rs. 2800

(d) Rs. 2840

**5.**

(a) 0

(b) 1

(c)

(d)

**6.**A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?

(a) 4 litres, 8 litres

(b) 6 litres, 6 litres

(c) 5 litres, 7 litres

(d) 7 litres, 5 litres

**7.**There is 80% increase in an amount in 8 years at simple interest. What will be the compound interest of Rs. 14,000 after 3 years at the same rate?

(a) Rs. 3794

(b) Rs. 3714

(c) Rs. 4612

(d) Rs. 4634

**8.**A vendor bought bananas at 6 for a rupee. How many for a rupee must he sell to gain 20%?

(a) 3

(b) 4

(c) 5

(d) 6

**9.**If 20% of a = b, then b% of 20 is the same as:

(a) None of these

(b) 10% of a

(c) 4% of a

(d) 20% of a

**10.**Father is aged three times more than his son Sunil. After 8 years, he would be two and a half times of Sunil’s age. After further 8 years, how many times would he be of Sunil’s age?

(a) 4 times

(b) 3 times

(c) 2 times

(d) 5 times

**Answer:**

1) (a) 2) (c) 3) (d) 4) (b) 5) (c)

6) (b) 7) (d) 8) (c) 9) (c) 10) (c)

**Explanation:**

1) (a)

N = H.C.F. of (4665 – 1305), (6905 – 4665) and (6905 – 1305)

= H.C.F. of 3360, 2240 and 5600 = 1120.

Sum of digits in N = (1 + 1 + 2 + 0) = 4

2) (c)

Let the speed of the train be

*x*km/hr and that of the car be*y*km/hr.
Solving (i) and (ii), we get:

*x*= 60 and*y*= 80.
Ratio of speeds = 60 : 80 = 3 : 4.

3) (d)

We need to know the S.I., principal and time to find the rate.

Since the principal is not given, so data is inadequate.

4) (b)

For managing, A received = 5% of Rs. 7400 = Rs. 370.

Balance = Rs. (7400 – 370) = Rs. 7030.

Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)

= 39000 : 42000 : 30000

= 13 : 14 : 10

5) (c)

=

=

= 1.

6) (b)

Let the cost of 1 litre milk be Re. 1

Milk in 1 litre mix. in 1

^{st}can = ¾ litre, C.P. of 1 litre mix. in 1^{st}can Re. ¾
Milk in 1 litre mix. in 2

^{nd}can = ½ litre, C.P. of 1 litre mix. in 2^{nd}can Re. ½
Milk in 1 litre of final mix. = 5/8 litre, Mean price = Re. 5/8

By the rule of alligation, we have:

C.P. of 1 litre mixture in 1st can & C.P. of 1 litre mixture in 2nd can

Ratio of two mixtures = = 1 : 1

So, quantity of mixture taken from each can = = 6 litres

7) (d)

Let P = Rs.100

Simple Interest = Rs. 80 (∵ 80% increase is due to the simple interest)

Rate of interest=100×SIPT=100×80100×8=10% per annum

Now let’s find out the compound interest of Rs. 14,000 after 3 years at 10%

P = Rs.14000

T = 3 years

R = 10%

Amount after 3 years = P = 14000

=14000 = 14000 = 14× = 18634

Compound Interest = Rs.18634 – Rs.14000 = Rs.4634

8) (c)

CP of 6 bananas = 1

Gain = 20%

SP of 6 bananas=1×120/100=1210

⇒The number of bananas he should sell for Rs.1 for a gain of 20% = = 10/2 = 5

9) (c)

20% of a = b

b =

b% of 20 = = = = = 4% of a

10) (c)

Assume that Sunil’s present age = x.

Then father’s present age = 3x + x = 4x

After 8 years, father’s age = 212 times of Sunil’s’ age

=> (4x+8) = 212(x+8)

=> 4x + 8 = 52(x + 8)

=> 8x + 16 = 5x + 40

=> 3x = 40 – 16 = 24

=> x = 243 = 8

After further 8 years,

Sunil’s age = x + 8 + 8 = 8 + 8 + 8 = 24

Father’s age = 4x + 8 + 8 = 4 × 8 + 8 + 8 = 48

Father’s age/Sunil’s age = 4824 = 2

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