**1.) 15 years ago, P was half of Q’s age. If the ratio of their present ages is2:3, what will be the total of their present ages?**

- 15
- 75
- 65
- 25

### Solution & Explanation

**Answer:** B**Explanation:**

Let present age of P and Q be 2x and 3x respectively.

15 years ago, P was half of Q’s age

(2x – 15) = ½ (3x – 15)

- 4x – 30 = 3x – 15
- 4x – 3x = – 15 +30
- x = 15

Now, total of their present ages

= 2x + 3x = 5x = 15 × 5 = __75__

**2.) A man’s age is140% of what it was 20 years ago, but 76% of what it will be after 20 What is his present age?**

- 70
- 50
- 40
- 60

### Solution & Explanation

**Answer:** A**Explanation:**

Age before 20 years = X.

140 X / 100 = X + 20

- 140 X = 100 X + 2000
- 40 X = 2000
- X = 50

Now the present age = X + 20

= 50 + 20 = __70__

**3.) A bill for Rs. 3000 is drawn on 14 ^{th}July at 5 months. It is discounted on 5^{th} October at 10%. What is the Banker’s Discount?**

- 40
- 50
- 60
- 70

### Solution & Explanation

**Answer:** C**Explanation:**

F = Rs. 3000

R = 10%

Date on which the bill is drawn = 14th July at 5 months

Nominally Due Date = 14th December

Legally Due Date = 14th December + 3 days = 17th December

Date on which the bill is discounted = 5th October

Unexpired Time

= [6th to 31st of October] + [30 Days in November] + [1st to 17th of December]

= 26 + 30 + 17

= 73 Days

= 73 / 365 year = 1/5 year

BD = Simple Interest on the face value of the bill for unexpired time

R x F x T /100

- 3000 x 1/5 x 10 /100
- 3000 x 2 / 100
- 6000 / 100

__60__

**4.) The banker’s gain on a certain sum due3 1/2 years hence is 8/26 of the banker’s discount. What is the rate percent?**

- 12 44/67 %
- 12 44/63 % ß
- 12 24/63 %
- 12 24/67 %

### Solution & Explanation

**Answer:** B**Explanation:**

T = 3 ½ à 7/2

Let the banker’s discount, BD = Rs. 1

Then, banker’s gain, BG = 8/26×1 = Rs. 8/26× 1

BG = BD – TD

⇒ 8/26 = 1 – TD

TD = 1 – 8 /26=18/26

F = BD ×TD/BD – TD

- 1 x 8/26 / 1 – 8/26
- 8/26 / 18/26
- 8/26 x26/18
- 18 / 8 Rs.

BD = Simple Interest on the face value of the bill for unexpired time = FTR/100

- 1 = 18/8 x 7/2 x R /100
- 100 = 18/8 x 7/2 x R
- 100 = 18 x 7 x R / 8 x 2
- 100 = 126 R / 16
- 100 x 16/ 126 = R
- 1600/126 = R
__12 44/63 %__

**5.) What digit will replace question mark –**

** 8, 10, 23, 73, 297, ?**

- 997
- 1491
- 1079
- 657

### Solution & Explanation

**Answer:** B**Explanation:**

8 x 1 = 8 + 2 = 10

10 x 2 = 20 + 3 = 23

23 x 3 = 69 + 4 = 73

73 x 4 = 292 + 5 = 297

297 x 5 = 1485 + 6 = __1491__

**6.) Ram started his leather shoes business with the amount of Rs. 2,50,000, 3 months later, his elder brother Shyam, joined him with the amount of Rs. 3,50,000. Now, at the end of the year, they got a profit of Rs. 4,00,00,000. Calculate the share of Shyam in profit. **

- 1,95,12,195.122
- 2,04,87,804.878 ß
- 1,52,34,589.322
- 2,45,65,342.578

### Solution & Explanation

**Answer:** B**Explanation:**

For 1 month, the ratio of equivalent capitals of both the brothers

= 250000 x 12 : 350000 x 9

= 20 : 21

And the total profit given = Rs. 40000000

So, the share of Shyam will be

= (21 / 20 + 21) x 40000000

= **Rs. 2,04,87,804.878**

**7.) In a 300 m race, A beats B by 22.5 m or 6 seconds. B’s time over the course is:**

- 60 sec
- 80 sec
- 40 sec
- 120 sec

### Solution & Explanation

**Answer:** B**Explanation:**

B runs 45/2 m in 6 sec

B covers 300 m in (6 x 2/45 x 300) sec = **80 sec**

**8.) Three taps Tap-1, Tap-2 and Tap-3 can fill a tank in 12, 15 and 20 hours respectively. If Tap-1 is open all the time and Tap-2 ,Tap-3 are open for one hour each alternatively, the tank will be full in:**

**5****7****6****8**

### Solution & Explanation

**Answer:** B**Explanation:**

Combined work of Tap-1 + Tap-2 for 1 four = 1/12 + 1/15 = 3/20

Combined work of Tap-1 + Tap-3 for 1 four = 1/12 + 1/20 = 2/15

So, their 2 hours’ work = 3/20 + 2/15

= 17 / 60

And 6 hours’ work = 17/60 x 3 = 17 / 20

And so the remaining part = 1 – 17/20 = 3/20

So, Tap-1+Tap-2 fills 3/20^{th} part in 1 hour, so the total time needed o fill the tank = 6+1 =**7 hrs.**

**9.) The reflex angle between the hands of a clock at 10.25 is-**

- 187 1/2°
- 197 1/2°
- 177 1/2°
- 178 1/2°

### Solution & Explanation

**Answer:** B**Explanation:**

Angle traced by hour hand in 125/12 hrs = (360/12 * 125/12) =312 ½ degree

Angle traced by minute hand in 25 min = (360/60 * 25) = 150 degree

So, Reflex angle = 360° – (312 ½ – 150)°

= 360° – 162 ½°

**= 197 ½°**

**10.) By how much is 1/5 of 430 smaller than 5/6 of 210?**

- 86
- 175
- 89
- 176

### Solution & Explanation

**Answer:** C**Explanation:**

**1/5 of 430 = 86 & 5/6 of 210 = 175**

175– 86 = **89**

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