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:

Q1. SOL: C

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 m2

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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