Question

A merchant completes a journey of total distance of 2400 km by using three modes: flight, train and bus. The
ratio of speeds of flight, train and bus is 40:5:3. The ratio of time spent on travel by flight, train and bus is
2:5:5. respectively. Find the distance travelled by train.​

Answer 1

Given :- A merchant completes a journey of total distance of 2400 km by using three modes: flight, train and bus. The ratio of speeds of flight, train and bus is 40:5:3. The ratio of time spent on travel by flight, train and bus is

2:5:5. respectively. Find the distance travelled by train.

Answer :-

Let speed by flight , train and bus is 40x , 5x and 3 kms and time taken by flight , train and bus is 2y hours , 5y and 5y hours .

A/q,

→ (40x * 2y) + (5x * 5y) + 3x * 5y = 2400

→ 80xy + 25xy + 15xy = 2400

→ 120xy = 2400

→ xy = 20 .

therefore,

→ Distance travelled by train = 25xy = 25 * 20 = 500 km (Ans.)

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Answer 2

SOLUTION

GIVEN

• A merchant completes a journey of total distance of 2400 km by using three modes: flight, train and bus.

• The ratio of speeds of flight, train and bus is 40 : 5 : 3

• The ratio of time spent on travel by flight, train and bus is 2 : 5 : 5 respectively.

TO DETERMINE

The distance travelled by train.

CONCEPT TO BE IMPLEMENTED

Ratio :

Ratio means comparing of two quantities

The ratio of a number a to another number b ( where b # 0) is a fraction a/b and it is written a : b , the first term a is called antecedent and the second term is called consequent

Compound Ratio :

For given two or three or more ratios, compound ratio is formed in such a way that the antecedent is the product of antecedent of the given ratios and consequent is the product of consequent of the given ratios

More precisely for given two ratios a : b & c : d the compound ratio is ac : bd

EVALUATION

Here it is given that a merchant completes a journey of total distance of 2400 km by using three modes: flight, train and bus.

Now the ratio of speeds of flight, train and bus is 40 : 5 : 3

Again the ratio of time spent on travel by flight, train and bus is 2 : 5 : 5 respectively.

We know that

Distance = Speed × Time spent

So the required ratio of distance is obtained by compounding the ratios of Speed and Time spent

Hence ratio of distance travelled in flight, train and bus is

= ( 40 × 2 ) : ( 5 × 5 ) : ( 5 × 3 )

= 80 : 25 : 15

= 16 : 5 : 3

Hence the required distance travelled in train

$\displaystyle \sf{ = 2400 \times \frac{5}{16 + 5 + 3} } \: \: km$

$\displaystyle \sf{ = 2400 \times \frac{5}{24} } \: \: km$

$\displaystyle \sf{ = 100 \times 5} \: \: km$

$\displaystyle \sf{ =500} \: \: km$

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