Ram and Mohan are friends. Each has some money. If Ram gives Rs 30 to

1.	Ram and Mohan are friends. Each has some money. If Ram gives Rs 30 to Mohan, then Mohan will have twice the money left with Ram. But if Mohan gives Rs 10 to Ram, then Ram will have thrice as much as is left with Mohan. How much money does each have ? (a) Rs 62, Rs 34 (b) Rs 6, Rs 2 (c) Rs 170, Rs 124 (d) Rs 43, Rs 26
Answer» (a) Rs 62, Rs 34 Let Ram have Rs x and Mohan have Rs y. If Ram gives Rs 30 to Mohan, then Ram has = Rs (x – 30) Mohan has = Rs (y + 30) According to the question, y + 30 = 2(x – 30) \(\Rightarrow\) y + 30 = 2x – 60 \(\Rightarrow\) 2x – y = 90 …....(i) If Mohan gives Rs 10 to Ram, then Ram has Rs (x + 10) Mohan has Rs (y – 10) According to the question, (x + 10) = 3(y – 10) \(\Rightarrow\)x + 10 = 3y – 30 \(\Rightarrow\) x – 3y = – 40 ........(ii) Now we can easily solve for x and y.

Ram and Mohan are friends. Each has some money. If Ram gives Rs 30 to Mohan, then Mohan will have twice the money left with Ram. But if Mohan gives Rs 10 to Ram, then Ram will have thrice as much as is left with Mohan. How much money does each have ? (a) Rs 62, Rs 34 (b) Rs 6, Rs 2 (c) Rs 170, Rs 124 (d) Rs 43, Rs 26

Answer»

(a) Rs 62, Rs 34

Let Ram have Rs x and Mohan have Rs y.

If Ram gives Rs 30 to Mohan, then

Ram has = Rs (x – 30)

Mohan has = Rs (y + 30)

According to the question, y + 30 = 2(x – 30)

\(\Rightarrow\) y + 30 = 2x – 60 \(\Rightarrow\) 2x – y = 90 …....(i)

If Mohan gives Rs 10 to Ram, then

Ram has Rs (x + 10)

Mohan has Rs (y – 10)

According to the question, (x + 10) = 3(y – 10)

\(\Rightarrow\)x + 10 = 3y – 30 \(\Rightarrow\) x – 3y = – 40 ........(ii)

Now we can easily solve for x and y.