[Download PDF] SRCC GBO 2017 Paper with Solutions

Instructions

For the following questions answer them individually

Question 61

If 6 years are subtracted from the present sate and the remainder is divided by 18, then the present age of his grandson Anupis obfainéd. If Anup is 2 years younger to Mahesh whose age is 5 years, whatis the age of Shyam?

Video Solution

Solution

Present age of Mahesh = 5 years

Present age of Anup = 5 - 2 = 3 years

Let present age of Suresh = S

Now,

$$\frac{S - 6}{18} = 3$$

S - 6 = 54

S = 60 years

Question 62

There are two concentric circular tracks of radii 100 m and 102 m respectively. A runs on the inner track and goes once round the track in 1 minute 30-seconds, while B runs on the outer track in 1 minute 32 seconds. Whoruns faster?

Video Solution

Solution

Let speed of A and B is 'a' m/s and 'b' m/s respectively.

Circumference of inner track = $$2\pi r = 200\pi$$ m

Circumference of outer track = $$2\pi r = 204\pi$$ mNow,

$$a = \frac{200\pi}{90} = 2.22\pi$$ m/s (Approx)

$$b = \frac{204\pi}{92} = 2.21\pi$$ m/s (Approx)

Hence, A is faster than B.

Question 63

A man observes that when he movesup distance C metres on a slope, the angle of depression of a point on the horizontal plane from the base of the slope is $$30^\circ$$, and when he moves up a further distance of C metres, the angle of depression of that point is $$45^\circ$$. The angle of inclination of the slope with the horizontal is ..........

Video Solution

Question 64

Out of 20 consecutive positive integers, two are chosen at random. The probability that their sum is odd is ..........

Video Solution

Solution

Out of 20 consecutive positive integers, 10 are even numbers and 10 odd numbers.

Sum is odd when one number of even and other is odd.

Favourable cases = $$10_{C_{1}} * 10_{C_{1}}$$ = 10 * 10

Total cases = $$20_{C_{2}}$$ = 10 * 19

Required probability = $$\frac{10 * 10}{10 * 19} = \frac{10}{19}$$

Question 65

A man covers a certain distance on a toy train. If the train moved 4 km/hr faster, it would take 30 minutes less. If it moved 2 km/hr slower, it would have taken 20 minutes more, What is the distance covered?

Video Solution

Solution

Let the time taken to cover 'D' km with speed S km/h is T hours.

D = ST

$$D = (S + 4) * (T - \frac{30}{60})$$

$$D = ST - \frac{S}{2} + 4T - \frac{4}{2}$$

$$D = D - \frac{S}{2} + 4T - \frac{4}{2}$$

8T - S = 4 ......... (1)

$$D = (S - 2) * (T + \frac{20}{60})$$

$$D = ST + \frac{S}{3} - 2T - \frac{2}{3}$$

$$D = D + \frac{S}{3} - 2T - \frac{2}{3}$$

S - 6T = 2 ......... (2)

From (1) and (2):

T = 3 and S = 20

D = ST = 60 km

Question 66

Two trains, 130 and 110 metres long, are going in the same direction. The faster train takes one minute to pass the other completely. If they are moving in opposite directions, they pass each other completely in 3 seconds. What is the speed of the faster train?

Video Solution

Solution

Let speed of faster and slower train is 'x' m/sec and 'y' m/sec respectibvely.

Now,

130 + 110 = (x - y) * 60

x - y = 4

130 + 110 = (x + y) * 3

x + y = 80

Speed of faster train = $$\frac{4 + 80}{2} = 42$$ m/sec

Question 67

The average age of all the students of a class is 18 years, The average age of boys of the class is 20 years and that of the girls is 15 years. If the number of girls in the class is 20, then what is the number of boys in the class?

Video Solution

Solution

Let total number of boys in the class = B

Now,

Average age of the class = $$18 = \frac{20 * B + 15 * 20}{B + 20}$$

18(B + 20) = 20B + 300

18B + 360 = 20B + 300

2B = 60

B = 30

Question 68

The total tractors in a State. are 294000, out of which 150000 are made by Mahindra & Mahindra. Out of every 1000: Mahindra tractors, 98 are red in colour, But only 5.3% of the total tractors are red. Find the percentage of non-Mahindrer tractors that are red.

Video Solution

Solution

Total tractors = 294000

Mahindra & Mahindra tractors = 150000

Non-Mahindra tractors = 294000 - 150000 = 144000

Total red colour Mahindra tractors = 150000 * $$\frac{98}{100} = 147000$$

Total red colour tractors = 53% of 294000 = 155820

Total red colour Non-Mahindra tractors = 155820 - 147000 = 8820

Required percent = $$\frac{8820}{144000} * 100 = 6.125$$%

Question 69

A merchant makesa profit of 20% by selling an article. What would be the approx. percentage change in the profit per cent had he paid 16% less for it and the customer paid 10% more for it?

Video Solution

Solution

Price at which merchant purchased = 100x

Price at which merchant sold = 120% of 100x = 120x

New price at which merchant purchased = 90% of 100x = 90x

New price at which merchant sold = 110% of 120x = 132x

New profit percent = $$\frac{132 - 90}{90} * 100 = 46.67$$%

Difference between profit percents = 46.67 - 20 = 26.67%

Required percent = $$\frac{26.67}{20} * 100 = 133.33$$%

Question 70

If 15 men or 24 women or 36 boys wah do a piece of work in 12 days, working 8 hours a day, how many men must be associated with 12 women and 6 boys to do another piece of work $$2\frac{1}{4}$$ times as great in 30 days working 6 hours a day?

Video Solution

Solution

15 men or 24 women or 36 boys wah do a piece of work in 12 days.

15M = 24W

1W = $$\frac{5}{8}$$M

15M = 36B

1B = $$\frac{5}{12}$$M

Let 'x' men are required.

Now,

$$2\frac{1}{4} * 15M * 12 * 8 = (xM +12W + 6B) * 30 * 6$$

$$\frac{9 * 15M * 12 * 8}{4} = (xM +7.5M + 2.5M) * 30 * 6$$

(x + 10) = 18

x = 8

CAT Content

SRCC GBO 2017

If 6 years are subtracted from the present sate and the remainder is divided by 18, then the present age of his grandson Anupis obfainéd. If Anup is 2 years younger to Mahesh whose age is 5 years, whatis the age of Shyam?

There are two concentric circular tracks of radii 100 m and 102 m respectively. A runs on the inner track and goes once round the track in 1 minute 30-seconds, while B runs on the outer track in 1 minute 32 seconds. Whoruns faster?

Out of 20 consecutive positive integers, two are chosen at random. The probability that their sum is odd is ..........

A man covers a certain distance on a toy train. If the train moved 4 km/hr faster, it would take 30 minutes less. If it moved 2 km/hr slower, it would have taken 20 minutes more, What is the distance covered?

Two trains, 130 and 110 metres long, are going in the same direction. The faster train takes one minute to pass the other completely. If they are moving in opposite directions, they pass each other completely in 3 seconds. What is the speed of the faster train?

The average age of all the students of a class is 18 years, The average age of boys of the class is 20 years and that of the girls is 15 years. If the number of girls in the class is 20, then what is the number of boys in the class?

The total tractors in a State. are 294000, out of which 150000 are made by Mahindra & Mahindra. Out of every 1000: Mahindra tractors, 98 are red in colour, But only 5.3% of the total tractors are red. Find the percentage of non-Mahindrer tractors that are red.

A merchant makesa profit of 20% by selling an article. What would be the approx. percentage change in the profit per cent had he paid 16% less for it and the customer paid 10% more for it?

If 15 men or 24 women or 36 boys wah do a piece of work in 12 days, working 8 hours a day, how many men must be associated with 12 women and 6 boys to do another piece of work $$2\frac{1}{4}$$ times as great in 30 days working 6 hours a day?

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