Direction (1 to 5 ): Study the following information carefully and answer the questions given beside:
There are four studios P, Q, R and S of renowned news channel “The Republic TV”. The number of reporters in studio S is 450 more than the number of reporters in studio R and 1650 less than the number of reporters in studio P. The number of reporters in studio Q is 24 more than 4.6 times of the number of computer operators in that studio. The number of reporters in studio R is 60 less than 3.8 times the no. of computer operators in studio S. The number of computer operators in studio S is 125 more than that of computer operators in studio P and 160 less than that of computer operators in studio Q. The number of computer operators in studio P and that in studio R are 825 and 1200 respectively.
The number of male reporters in studio P is 40% of the total number of reporters in studio Q. The number of female computer operators in studio P is 48% of the total number of computer operators in studio S. The number of male reporters in studio R is 5 times of the number of female computer operators in studio P. The number of male reporters in studio S is double the number of female reporters in studio R. The number of male reporters in studio Q is 2250 more than the number of male reporters in studio R. The number of male computer operators in studio Q is 16% of the total number of reporters of studio S. The number of female computer operators in studio R is 60 less than that of male computer operators in studio Q. The number of male computer operators in studio S is 1.5 times that of female computer operators in studio Q.
Q1. What is ratio of the number of female reporters in studio P and Q together to the number of female reporters in studio R and S together?
A) 25 : 16
B) 34 : 35
C) 45 : 46
D) 114 : 125
E) 117 : 135
Q2. What is the approximate sum of the average number of female computer operators in studio Q, R and S together and, the average number of male reporters in those studios?
A) 3548
B) 4538
C) 3575
D) 3355
E) 3575
Q3. The number of female computer operators in studios P, R and S together is approximate what per cent of the number of male reporters in studios P and S together?
A) 25%
B) 21%
C) 13%
D) 17%
E) 21%
Q4. What is the difference between the number of male reporters in studios P, Q and R together and the number of male computer operators in all the studios together?
A) 8074
B) 8064
C) 8054
D) 8044
E) 8014
Q5. In which studio are male reporters the maximum and female computer operators the minimum respectively?
A) Q &R
B) Q & S
C) R & P
D) None of these
E) P & Q
Q6. Kohali bought a car for Rs.1000x and sold it to Modi at x% profit. Modi didn’t like the car and sold it back to Kohali at 70% of the price at which he had bought from Kohali. In this entire transaction, Kohali made a profit of 33%. What was the cost price of the car for him (in rupees)?
A) 8000 Rs.
B) 10000 Rs.
C) 9600 Rs.
D) 8800 Rs.
E) 11200 Rs.
Q7. Akash, Binod and Chandan together can complete a work in 10 days. Binod alone can complete the work in 20 days, while Chandan alone can complete the work in 30 days. Akash and Binod started the work and every alternate day Akash was replaced by Chandan. If they received Rs. 12000 for the work, what was Chandan’s share in earning from the work?
A) 2580 Rs.
B) 2460 Rs.
C) 2240 Rs.
D) 2148 Rs.
E) 2560 Rs.
Q8. The normal speed of two motorists Doraemon and Nobita Nobi is 160 Km/h and 200 Km/h. Doraemon starts at the speed, 50% lower than his normal speed and increases his speed by 25% after finishing every quarter of the race. Nobita Nobi starts at the speed of 80% of his normal speed and increases his speed by 25%, after finishing half of the race. If both the motorists start together and Doraemon finished the race 25.92 minutes before Nobita Nobi did, what was the length of the track?
A) 160 km
B) 100 km
C) 120 km
D) 80 km
E) 180 km
Q9. In a dhaba, any person eating chapati has to pay a fixed charge and an additional amount proportional to the number of chapati eaten. But if one eats more than 60 chapati per month, one has to additionally pay an amount proportional to the square root of number of chapati eaten. If a person pays Rs.400 for 50 chapati, Rs.360 for 30 chapati and Rs.498 for 81 chapati, how much should he pay for 100 chapati (in Rs.)?
A) 520 Rs.
B) 580 Rs.
C) 640 Rs.
D) 540 Rs.
E) 720 Rs.
Q10. In Delhi public school each student opted for either physical education or yoga extra subject in school. 60% of the girls and 50% of the boys opted for physical education, whereas 50% of the girls and 55% of the boys opted for yoga. The number of students who opted for physical education was six more than those who opted for yoga. The number of girls who opted for yoga was more than the number of boys who opted for yoga. If the difference between the number of boys and number of girls who opted for yoga and the difference between the number of boys and number of girls who opted for physical education were in the ratio 9 : 14, what is the total number of students in the school ?
A) 120
B) 140
C) 160
D) 180
E) 220
Solution.
Q(1 to 5) :
Common Explanation: As per the given information, we can create a table
| Studios | Reporters | Comp. Operators | ||||
| Total | M | F | Total | M | F | |
| P | 4000 + 1650 = 5650 | 40% of 5130 = 3598 | 5650 – 3598 = 2052 | 825 | 825 – 456 = 369 | 48% of 950 = 456 |
| Q | 1110 × 4.6 + 24 = 5130 | 2280 + 2250 = 4530 | 5130 – 4530 = 600 | 950 + 160 = 1110 | 16% of 4000 = 640 | 1110 – 640 = 470 |
| R | 950 × 3.8 – 60 = 3550 | 456 × 5 = 2280 | 3550 – 2280 = 1270 | 1200 | 1200 – 580 = 620 | 640 – 60 = 580 |
| S | 3550 + 450 = 4000 | 2 × 1270 = 2540 | 4000 – 2540 = 1460 | 825 + 125 = 950 | 470 × 1.5 = 705 | 950 – 705 = 245 |
Q1. Ans(B)
Explanation:
Following the common explanation, we get
Total number of female reporters in studio P = 2052
Similarly, in Q = 600
And, Total number of female reporters in R = 1270
Similarly, in S = 1460
| Required ratio = | 2052 + 600 | = | 2652 | = 34 : 35 |
| 1270 + 1460 | 2730 |
Q2. Ans(A)
Explanation:
Following the common explanation, we get
Total no. of female computer operators in Q, R and S = 470 + 580 + 245 = 1295
Total no. of male reporters in Q, R and S = 4530 + 2280 + 2540 = 9350
| ∴ Required average = | 1295 + 9350 | = | 10645 | = 3548.33 ≈ 3548 |
| 3 | 3 |
Q3. Ans(E)
Explanation:
The total number of female operators in studio P = 456
Similarly, In R = 580 and In S = 245
And, The total number males reporters in P = 3598 and in S = 2540
| ∴ Required % = | 456 + 580 + 245 | × 100 |
| 3598 + 2540 |
| = | 1281 | × 100 = 20.86 ≈ 21% |
| 6138 |
Q4. Ans(A)
Explanation:
Total no. of male reporters in studio P = 3598
Similarly, in studio Q = 4530 and in studio R = 2280
Therefore, total no. of reporters in studios P, Q and R together = 3598 + 4530 + 2280 = 10408
And the total no. of male computer operators in studio P = 369
Similarly, in studio Q = 640, In studio R = 620 and in studio S = 705
Therefore, total no. male computer operators in studios P, Q, R and S together = 369 + 640 + 620 + 705 = 2334
∴ Required difference = 10408 – 2334 = 8074
Q5. Ans(B)
Explanation:
Following the common explanation, we get
That in the studio Q male reporters are maximum which is 4530
And, in the studio S has the least female computer operators which is 245.
Q6. Ans(B)
Explanation:
Given that cost price of Kohali = 1000x
Selling price of Kohali = 1000x + (1000x × x%)
| = 1000x + | 1000x × x | = 1000x + 10 x2 |
| 100 |
Cost price of Modi = 1000x + 10 x2
Selling price of Modi = 70% of (1000x + 10 x2)
| = | 70 | × (1000x + 10x2) = 700x + 7x2 |
| 100 |
Kohali was left with (1000x + 10 x2) – (700x + 7x2) = (300x + 3x2) after paying to Modi, that is the profit of Kohali.
According to question,
(300x + 3x2) = 33% of (1000x)
| ⇒ (300x + 3x2) = | 33 | × 1000x |
| 100 |
⇒ (300x + 3x2) = 330x
⇒ 3x2 = (330x – 300x) = 30x
⇒ X = 10
Thus, cost price of car for Kohali = 1000x = (1000 × 10) = Rs. 10000
Q7. Ans(E)
Explanation:
Let the total work be 60 unit (LCM of 10, 20 and 30)
| Work done by Binod in one day = | 60 | = 3 units |
| 20 |
| Work done by Chandan in one day = | 60 | = 2 units |
| 30 |
Let work done by Akash in one day = a
From question
(a + 2 + 3) × 10 = 60
⇒ a = 1 unit
When Akash and Binod started the work and every alternate day Akash was replaced by Chandan
Work done on 1st day = 1 + 3 = 4
Work done on 2nd day = 2 + 3 = 5
Work done in 2 days = 9 units
Work done in 12 days = 54 units
On 13th day Akash and Binod will work i.e. on 13th day 4 units of work was done
On 14th day Chandan and Binod will work i.e. on 14th day 2 units of work was done
When Chandan & Binod together work for whole day, 5 units of work is done out of which 2 units is done by Chandan
So, When Chandan & Binod together work and 2 units of work is done, work done by Chandan
| = | 2 | × 2 = 0.8 units |
| 5 |
Total work done by Chandan during the work = 2 × 6 + 0.8 = 12.8 units
| Therefore, Chandan’s share = | 12.8 × 12000 | = Rs. 2560 |
| 60 |
Q8. Ans(C)
Explanation:
Let the track length be 4d
Time take by Doraemon to finish the race
| = | d | + | d | + | d | +… |
| 160 × 0.5 | 160 × 0.5 × 1.25 | 160 × 0.5 × 1.25 × 1.25 |
| …+ | d |
| 160 × 0.5 × 1.25 × 1.25 × 1.25 |
| = | d | + | d | + | d | + | d |
| 80 | 100 | 125 | 156.25 |
Time take by Nobita Nobi to finish the race
| = | 2d | + | 2d | = | d | + | d |
| 200 × 0.8 | 200 × 0.8 × 1.25 | 80 | 100 |
From question,
| ( | d | + | d | + | d | + | d | ) | – | ( | d | + | d | ) | = | 25.92 |
| 80 | 100 | 125 | 156.25 | 80 | 100 | 60 |
| ⇒ | d | + | d | = | 25.92 |
| 125 | 156.25 | 60 |
| ⇒ | 1.25d | + | d | = | 25.92 |
| 156.25 | 156.25 | 60 |
| ⇒ | 2.25 | d = | 25.92 |
| 156.25 | 60 |
| ⇒ d = | 25.92 × 156.25 | = 30 |
| 60 × 2.25 |
Therefore, track length = 4d = 4 × 30 = 120 Km
Q9. Ans(D)
Explanation:
Let amount paid = Rs. x
Fixed charge = Rs. y
Number of chapati eaten = n
If anyone eat less than 60 chapati per month, then
Amount paid (x) = fixed charge (y) + k1 × (number of chapati eaten)
Where Let the number of boys and girls in the school be denoted by “b” and “g” respectively.
k1 being the constant of proportionality
i.e, x = y + k1 × n
according to the question,
400 = y + 50 × k1……… (i)
360 = y + 30 × k1……….(ii)
If anyone eats more than 60 chapati per month, then
X = y + k1 × n + k2 × √n, where k2 being the constant of proportionality
Now, 498 = y + 81k1 + k2 × √81
⇒ 498 = y + 81k1 + 9k2 …….. (iii)
After solving (i) and (ii), we get
20 k1 = 40 ⇒ k1 = 2 and y = (400 – 50 × 2) = 300
Substituting the value of y and k1 in (iii), we get
498 = 300 + (81 × 2) + 9k2 ⇒ k2 = ((498 – 462)/9) = 4
Thus, amount of bill for 100 chapati is
X = y + k1 × n + k2 × √n = 300 + (100 × 2) + (4 × √100) = 300 + 200 + (4 × 10) = Rs. 540
Q10. Ans(A)
Explanation:
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