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Pair of Linear Equations in Two Variables

Short Answer Type

201. Places A and B are 100 km. apart on a highway. On car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars ?

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202. The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each saves Rs. 200 per month find their monthly incomes.

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203. A man travels 370 km partly by train and partly by car. If he covers 250 km by train and the rest by car, it takes him 4 hours. But, if he travels 130 km by train and the rest by car, he takes 18 minutes longer. Find the speed of the train and that of the car.

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204. The sum of a two-digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there?

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205.

Solve the following system of equations by elimination method

6(ax + by) = 3a + 2b
6(bx - ay) =3b - 2a.

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206. A man has only 20 paisc coins and 25 paise coins in his purse. If he has 50 coins in all, totalling Rs. 11.25. How many coins of each type does he share ? (Use Elimination Method).

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207. A person starts his job with a monthly income and earns a fixed increment every year. If his salary was Rs. 4500 after 4 years of service and Rs. 5400 after 10 years of service, find the initial salary and the annual increment by using elimination method.

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208.
A motor boat whose speed is 24 km/h in still water takes 1 hour more to go 32km upstream than to return downstream to the same spot. Find the speed of the stream.

Let the speed of the stream be s km/h.
Speed of the motor boat 24 km / h
Speed of the motor -boat upstream 24 s
Speed of the motor boat downstream 24 s
According to the given condition,

$fraction numerator 32 over denominator 24 minus straight s end fraction minus fraction numerator 32 over denominator 24 plus s end fraction space equals 1 therefore space 32 space open parentheses fraction numerator 1 over denominator 24 minus s end fraction minus fraction numerator 1 over denominator 24 plus s end fraction close parentheses equals 1 therefore space 32 space open parentheses fraction numerator 24 plus straight s minus 24 plus straight s over denominator 576 minus straight s squared end fraction close parentheses space equals 1 therefore space 32 space straight x space 2 straight s space equals 576 minus straight s squared therefore space straight s squared plus 64 straight s minus 576 space equals 0 therefore space left parenthesis straight s plus 72 right parenthesis left parenthesis straight s minus 8 right parenthesis space equals 0 Therefore comma space straight s equals negative 72 space ors equals 8$

Since, speed of the stream cannot be negative, the speed of the stream is 8 km/h.

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Long Answer Type

209. A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

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