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TATA Motors (A Car manufacturing company) manufactured only two brands of cars A and B in the year 2016. In the year 2017, it introduced a new brand of car C. The number of cars of brands A and that of brand B manufactured in the year 2016 was in the ratio of 4: 5 respectively. The number of cars of brand A manufactured in the year 2016 to that in the year 2017 was in the ratio of 3: 2 and the number of cars of brand B manufactured in the year 2016 to that in the year 2017 was in the ratio of 3: 4. Further, the total number of cars manufactured in the year 2017 of brand C forms 30% of the total number of cars manufactured in the year 2017.

Important for :

1

B

Following common explanation, we getIn the year 2016, The total number of cars of brand A manufactured = 4x = 1800

x = | 1800 | = 450 |

4 |

The total number of cars manufactured of brand A and B in the year 2017

= | 8x | + | 20x | = | 28x | = | 28 × 450 | = 4200 |

3 | 3 | 3 | 3 |

Let the total number of cars manufactured of brand C in the year 2017 = c then

c = 30% of (4200 + c)

100c = 30 × 4200 + 30c

70c = 30 × 4200

c = 30 × 60 = 1800

Hence , option B is correct.

Let in the year 2016, The total number of cars of brand A manufactured = 4x then the total number of cars of brand B manufactured in that year = 5x

Let in the year 2017, total number of cars manufactured of brand A = P and that of brand B = Q then according to the question

4x : P = 3 : 2

8x = 3P

P = | 8x |

3 |

For the brand B,

5x : Q = 3 : 4

20x = 3Q

Q = | 20x |

3 |

= total number of cars manufactured of brand B in the year 2017

2

C

Following common explanation, we getThe total number of cars of all the brands manufactured in the year 2017

= | 8x | + | 20x | + c = | 28x | + c |

3 | 3 | 3 |

where c = total number of cars manufactured of brand C in the year 2017

c = 30% of | ( | 28x | + c | ) |

3 |

100c – 30c = 70c = 30 × | 28x |

3 |

c = | 12x |

3 |

the total number of cars of all the brands manufactured in the year 2017

= | 8x | + | 20x | + c = | 28x | + | 12x | = | 40x |

3 | 3 | 3 | 3 | 3 |

the total number of cars of all the brands manufactured in the year 2016 = 4x + 5x = 9x the required percentage increase

( | 40x | – 9x | ) | ||||||

= | 3 | × 100 = | 13 | × 100 = | 1300 | = 48.15% approximately | |||

9x | 27 | 27 |

Hence, option C is correct.

Let in the year 2016, The total number of cars of brand A manufactured = 4x then the total number of cars of brand B manufactured in that year = 5x

Let in the year 2017, total number of cars manufactured of brand A = P and that of brand B = Q then according to the question

4x : P = 3 : 2

8x = 3P

P = | 8x |

3 |

For the brand B,

5x : Q = 3 : 4

20x = 3Q

Q = | 20x |

3 |

= total number of cars manufactured of brand B in the year 2017

3

E

Following common explanation, we getThe total number of cars of all the brands manufactured in the year 2017

= | 8x | + | 20x | + c = | 28x | + c |

3 | 3 | 3 |

= 30% of | ( | 28x | + c | ) |

3 |

100c – 30c = 70c = 30 × | 28x |

3 |

c = | 12x | = 900 |

3 |

x = | 900 | = 225 |

4 |

the total number of cars of all the brands manufactured in the year 2017

= | 8x | + | 20x | + c = | 28x | + | 12x | = | 40x | = | 40 × 225 | = 3000 |

3 | 3 | 3 | 3 | 3 | 3 |

In the next year i.e. in the year 2018, TATA Motors wants to increase its car manufacturing capacity by 25% compare to the previous year

Therefore, in the year 2018, the total number of cars it will manufacture = 125% of 3000 = 3750

It doesn’t make ang changes in any brand therefore the total number of brand D cars it will manufacture = 3750 – 3000 = 750

Hence, option E is correct.

Let in the year 2016, The total number of cars of brand A manufactured = 4x then the total number of cars of brand B manufactured in that year = 5x

Let in the year 2017, total number of cars manufactured of brand A = P and that of brand B = Q then according to the question

4x : P = 3 : 2

8x = 3P

P = | 8x |

3 |

For the brand B,

5x : Q = 3 : 4

20x = 3Q

Q = | 20x |

3 |

= total number of cars manufactured of brand B in the year 2017

4

D

Following common explanation, we getThe total number of cars of brands C manufactured in the year 2017 = 4% of 7000 = 280

The total number of cars manufactured of brand A and B in the year 2017

= | 8x | + | 20x | = | 28x | = 7000 – 280 = 6720 |

3 | 3 | 3 |

x = | 6720 × 3 | = 240 × 3 = 720 |

28 |

total cars of brand A manufactured in the years 2016 and 2017 together

= 4x + | 8x | = | 20x | = | 20 × 720 | = 4800 |

3 | 3 | 3 |

Hence, option D is correct.

Let in the year 2016, The total number of cars of brand A manufactured = 4x then the total number of cars of brand B manufactured in that year = 5x

Let in the year 2017, total number of cars manufactured of brand A = P and that of brand B = Q then according to the question

4x : P = 3 : 2

8x = 3P

P = | 8x |

3 |

= total number of cars manufactured of brand A in the year 2017

For the brand B,

5x : Q = 3 : 4

20x = 3Q

Q = | 20x |

3 |

= total number of cars manufactured of brand B in the year 2017

5

B

Following common explanation, we get20x/3 = total number of cars manufactured of brand B in the year 2017

20x | = 900 |

3 |

x = 45 × 3 = 135

the total number of cars of all the brands manufactured in the year 2017

= | 8x | + | 20x | + c = | 28x | + | 12x | = | 40x |

3 | 3 | 3 | 3 | 3 |

the total number of cars of all the brands manufactured in the year 2016 = 4x + 5x = 9x

The reqd. sum = 9x + | 40x | = | 67x | = 67 × | 135 | = 45 × 67 = 3015 |

3 | 3 | 3 |

Hence, option B is correct.

Let in the year 2016, The total number of cars of brand A manufactured = 4x then the total number of cars of brand B manufactured in that year = 5x

Let in the year 2017, total number of cars manufactured of brand A = P and that of brand B = Q then according to the question

4x : P = 3 : 2

8x = 3P

P = | 8x |

3 |

= total number of cars manufactured of brand A in the year 2017

For the brand B,

5x : Q = 3 : 4

20x = 3Q

Q = | 20x |

3 |

= total number of cars manufactured of brand B in the year 2017

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