**Q1. A train of length (x + 30) m can cross a man standing on the platform in 12 sec and, it can pass a man who is moving at speed of 18 Km/hour in same direction that of train, in 15 sec, find the length of train.**

A 240 m

B 270 m

C 300 m

D 360 m

E None of these

**Q2. A, B and C can do a work individually in 12 days, 15 days and 20 days respectively. A, B and C together started the work and worked for 2.5 days and then B and C left the work. If A works for ‘x’ days after B and C left the work and the remaining work is completed by B alone after A has worked for x days, then find the value of ‘x’. The total work is completed in 9.4 days.**

A 2.25 days

B 2.2 days

C 2 days

D 2.4 days

E None of these

**Q3. A train crosses a bridge of length ‘x’ metres at the speed of 72 km/hr in 72.5 seconds. If the train crosses a man standing on the platform at the same speed in 32 seconds, then find the value of ‘x’.**

A 980 metres

B 850 metres

C 810 metres

D 740 metres

E None of these

**Q4. The cost price of ‘x’ litres of oil is Rs. 16/litre. If 2 litres of freely available water is mixed to the oil and the whole mixture is sold at the price of Rs. 15.2/litre such that there is no loss or profit, then find the value of ‘x’.**

A 32 litres

B 28 litres

C 33 litres

D 36 litres

E None of these

**Q5. The population of a village consisting of males and females is ‘x’. If the female population in the village is 45% and the difference between the male population and female population is 440, then find the value of ‘x’.**

A 4800

B 4000

C 4600

D 4400

E None of these**Q6.Five years ago, the average age of Raj, Simran and Babuji was 31 years. At present, the average age of the family is reduced by 3 years and it was due to the birth of Raj and Simran’s son Shahrukh during the 5 year period. Find the present age of Shahrukh.**

A 5 years

B 3 years

C 2 years

D 6 years

E 4 years**Q7. Difference between the compound interest and simple interest earned on a similar sum after two years is Rs.162. If in both the cases the interest rate was 9% p.a. then, find the principal amount invested in each interest scheme?**

A Rs. 5000

B Rs. 15000

C Rs. 18000

D Rs. 20000

E Rs. 22500**Q8. Q8. The cost price of a book is Rs. 620. The shopkeeper sells the book at a profit of 15%. If the marked price of the book is Rs. 975 then find the difference between the selling price and the marked price of the book.**

A Rs. 245

B Rs. 262

C Rs. 284

D Rs. 289

E Rs. 277**Q8. The cost price of a book is Rs. 620. The shopkeeper sells the book at a profit of 15%. If the marked price of the book is Rs. 975 then find the difference between the selling price and the marked price of the book.**

A Rs. 245

B Rs. 262

C Rs. 284

D Rs. 289

E Rs. 277

**Q9. The perimeter of a rectangular park is 142 m. If the difference between the length and the breadth of the park is 9 m then find the area of the rectangular park.**

A 1152 m

B 1428 m

C 1140 m

D 1240 m

E 1320 m

D. 1240 m

**Q10. A can do a piece of work in 12 days, while B and C together can complete the work in 8 days. If A and C together can complete the work in 6 days, then find the time taken by B alone to complete half the work.**

A. 8 days

B. 12 days

C. 6 days

D. 9 days

E. None of these

**Solution:**

Let, the speed of train is ‘s’ m/s

According to question,

(x + 30)/12 = s

And, (x + 30)/15 = s – 18 × (5/18)

Therefore, comparing both equations, we get,

(x + 30)/12 = (x + 30)/15 + 18 × (5/18)

(x + 30)/12 = (x + 30 + 75)/15

5x + 150 = 4x + 420

5x – 4x = 420 – 150

x = 270

Therefore, length of train = 270 + 30 = 300 m

Q2. SOL: D

Let the total work be LCM of (12, 15 and 20) = 60 units

Number of units of work completed by A in one day = 5 units

Number of units of work completed by B in one day = 4 units

Number of units of work completed by C in one day = 3 units

Number of units of work completed by A, B and C together in one day = (5 + 4 + 3)

= 12 units

According to question,

12 × 2.5 + 5x + 4(9.4 – 2.5 – x) = 60

=> 30 + 5x + 4(6.9 – x) = 60

=> 30 + 5x + 27.6 – 4x = 60

=> x = 60 – 57.6

=> x = 2.4 days

Q3. SOL: C

Speed of train = 72 km/hr = 20 m/s

Length of the train = 20 × 32 = 640 metres

According to question,

(640 + x) = 20 × 72.5

640 + x = 1450

x = 810 metres

Q4. SOL: E

According to question,

16x = 15.2 (x + 2)

=> 16x = 15.2x + 30.4

=> 0.8x = 30.4

=> x = 38 litres

Q5. SOL: D

Given, total population of the village = x

Female population = 45% of x = 0.45x

Male population = 55% of x = 0.55x

According to question,

0.55x – 0.45x = 440

=> 0.1x = 440

=> x = 4400

Q6. SOL: E

According to question,

Raj + Simran + Babuji = 31×3 = 93

New Average = 31 – 3 = 28

Therefore, after 5 years,

(Raj+5) + (Simran+5) + (Babuji+5) + Shahrukh = 28 × 4 = 112

Shahrukh = 112 – 15 – 93 = 4 years

Q7. SOL: D

Let the principal be P.

Simple Interest for 2 years = P × 0.09 × 2 = 0.18P

Compound Interest for 2 years = P [(1.09) – 1] = 0.1881P

0.1881P – 0.18P = 162

0.0081P = 162, P = Rs.20000
Q8. SOL: B

Selling price of the book = 115% of 620 = Rs. 713

Required difference = 975 – 713 = Rs. 262

Q9. SOL: D

Let, the breadth of the park = x m

Then, the length of the park = (x + 9) m

So, 2 * (x + x + 9) = 142

=>2 * (2x + 9) = 142

=>4x + 18 = 142

=>4x = 142 – 18

=>4x = 124

=>x = 31

Therefore, the breadth of the park = 31 m

And, the length of the park = 40 m

So, area of the park = 40 * 31 = 1240 m

^{2}
Q10. SOL: B

Let, the total work be LCM
of (12, 8 and 6) = 24 units

Number of units of work
completed by A alone in one day = 24 ÷ 12 = 2 units

Number of units of work
completed by B and C together in one day = 24 ÷ 8 = 3

units

Number of units of work
completed by A and C together in one day = 24 ÷ 6 = 4

units

Number of units of work
completed by C alone in one day = 4 – 2 = 2 units

Number of units of work
completed by B alone in one day = 3 – 2 = 1 unit

Required time taken to
complete half the work = (24 ÷ 2) ÷ 1 = 12 days

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