Question :

A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.

Maths

Class 10

##### Views

887

Georgia

Vedhika

Solution: Let

The cost of 1st prize be Rs.P and cost of 2nd prize = Rs.P − 20, and cost of 3rd prize = Rs.P − 40.
We can see that the cost of these prizes is in the form of A.P. Therefore, first term is P and common difference (P − 40) − (P − 20) = −40 + 20 = −20. Thus, a = P and d = −20

Also given that the som of 7 ters are 700, that is S7 = 700. By the formula of sum of nth term, we know the formula Sn = n/2 [2a + (n – 1)d]. Replace the values weget,

7/2 [2a + (7 – 1)d] = 700

7/2 [2a + (6) (–20)] = 700

2a + 6(−20) = 200
2a − 120 = 200
2a = 320 ⇒ a = 160

Therefore, the value of each of the prizes was Rs 160, Rs 140, Rs 120, Rs 100, Rs 80, Rs 60, and Rs 40.

Seema

Let the least value price be X.

Then the next value is X + 20, and the next value is X + 40 and on and on up to 7 values.

Using an arithmetic Progression with sum 700. You can do it either manually or using the formula of AP.

Method 1: (Manually)

X + X+20 + X + 40 + …  X + 120 = 700

⇒ 7X + (20 + 40 + … + 120) = 700

⇒ 7X + 20(1 + 2 + 3 + … + 6) = 700

⇒ 7X + 20(21) = 700

⇒ 7X = 280

⇒ X = 40

Method 2: (Using AP Formula)

Number of prizes = 7 (N). So sum till nth term will be:

n/2 (2X+ (n - 1) x 20) = 700.

Put the value of N as 7.

⇒ 7/2 (2X + 120) = 700

⇒ (2X + 120) = 700 * 2/7

⇒ 2X + 120 = 200

⇒ 2X = 200 - 120

⇒ 2X = 80

⇒ X = 40

## Advantages Of NCERT, CBSE & State Boards Solutions For All Subjects

• All the NCERT Solutions have been prepared by academic experts having 10+ years of teaching experience.
• They have prepared all the solutions in simple and easy language so that each and every student can understand the concepts easily.
• All the solutions have been explained step to step-wise in details with better explanations.
• Students can also use these question and answers for your assignments and in homework help.
• All the solutions have been explained in detail and the answers have been compiled in a step-wise manner.
• All the questions and answers are commonly prepared according to the Latest Syllabus of Board Education and Guidelines.
• Students can know about the various types of questions asked in the exams with the help of these solutions.