a. Two numbers are in the ratio 6:5. If the sum of the numbers is 110, find the numbers.
b. Hari's father gave him Rs 70. Now, he has Rs 130. How much money did Hari have in the beginning?
Answers
QUESTION A :
Given :
• Two numbers are in the ratio 6 : 5
• The sum of both the numbers is 110
To Find :
• The numbers
Solution :
Let the two numbers be 6x and 5x respectively.
we have,
→ 6x + 5x = 110
→ 11x = 110
→ x = 110/11
→ x = 10
This means that the numbers are :-
→ 6x = 6 x 10 = 60
→ 5x = 5 x 10 = 50
Verification :
LHS :
→ 6x + 5x
→ 6(10) + 5(10)
→ 60 + 50
→ 110
RHS = 100
LHS = RHS
Hence verified!
QUESTION B :
Given :
• Hari's father gave him Rs 70
• He has total Rs 130 now
To Find :
• The money he had earlier.
Solution :
Let the original sum of money he had earlier as Rs x
Hari's father gave him Rs 70
→ Original sum of money + Money given by Hari's father
→ x + 70
Total amount of money has now = 130
According to the question,
→ x + 70 = 130
→ x = 130 - 70
→ x = 60
Therefore, the original sum of money he had = Rs. 60
⚘ Qυꫀstíoꪀ :-
a. Two numbers are in the ratio 6:5. If the sum of the numbers is 110, find the numbers.
b. Hari's father gave him Rs 70. Now, he has Rs 130. How much money did Hari have in the beginning?
⚘ Soℓυtíoꪀ :-
a.)
➴ Given:- two numbers in the ratio 6:5 and their sum is 110.
↬ To find:- The numbers whose sum is 110 and are in the ratio of 6:5.
Now, let the two numbers be 6x and 5x respectively.
Then, 6x + 5x = 110
⇒ 11x = 110
⇒ x = 110/ 11
∴ x = 10
So, the numbers are :
6x = 6 × 10 = 60
and 5x = 5 × 10 = 50
━━━━━━━━━━ × ━━━━━━━━━━
b.)
➴ Given:- Money given by Hari's father is Rs. 70
and total amount of money he has now is Rs. 130.
↬ To find:- Money he had in the beginning.
Now, let the money Hari had in the beginning be x
Then, x + 70 = 130
⇒ x = 130 - 70
∴ x = 60
So, he had Rs. 60 in the beginning.